Proofs

A proof is a series of claims that lead to a conclusion. Some proofs are conditional, which means that the claims can only be made under certain conditions. Click on a statement to see the proof

Byte 8 Stays the Same 11
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 11 = 4
  • value of cell 8 at time 11 = 24

then value of cell 8 at time 12 = 24


Byte 9 Stays the Same 11
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 11 = 4
  • value of cell 9 at time 11 = 31

then value of cell 9 at time 12 = 31


Byte 10 Stays the Same 11
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 11 = 4
  • value of cell 10 at time 11 = 45

then value of cell 10 at time 12 = 45


Byte 7 Stays the Same 11
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 11 = 4
  • value of cell 7 at time 11 = 31

then value of cell 7 at time 12 = 31


Byte 12 Stays the Same 11
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 11 = 4
  • value of cell 12 at time 11 = 24

then value of cell 12 at time 12 = 24


Byte 13 Stays the Same 11
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 11 = 4
  • value of cell 13 at time 11 = 31

then value of cell 13 at time 12 = 31


Beq No Branch 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 3 at time 12 = 3
  • value of cell 4 at time 12 = 2

then the PC at time 13 = 6


Byte 3 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 3 at time 12 = 3

then value of cell 3 at time 13 = 3


Byte 4 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 4 at time 12 = 2

then value of cell 4 at time 13 = 2


Byte 5 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 5 at time 12 = 10

then value of cell 5 at time 13 = 10


Byte 6 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 6 at time 12 = 14

then value of cell 6 at time 13 = 14


Byte 8 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 8 at time 12 = 24

then value of cell 8 at time 13 = 24


Byte 9 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 9 at time 12 = 31

then value of cell 9 at time 13 = 31


Byte 10 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 10 at time 12 = 45

then value of cell 10 at time 13 = 45


Byte 7 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 7 at time 12 = 31

then value of cell 7 at time 13 = 31


Byte 12 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 12 at time 12 = 24

then value of cell 12 at time 13 = 24


Byte 13 Stays the Same 12
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 12 = 5
  • value of cell 13 at time 12 = 31

then value of cell 13 at time 13 = 31


Jump Help 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6

then the PC at time 14 = 0


Byte 3 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 3 at time 13 = 3

then value of cell 3 at time 14 = 3


Byte 4 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 4 at time 13 = 2

then value of cell 4 at time 14 = 2


Byte 5 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 5 at time 13 = 10

then value of cell 5 at time 14 = 10


Byte 6 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 6 at time 13 = 14

then value of cell 6 at time 14 = 14


Byte 8 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 8 at time 13 = 24

then value of cell 8 at time 14 = 24


Byte 9 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 9 at time 13 = 31

then value of cell 9 at time 14 = 31


Byte 10 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 10 at time 13 = 45

then value of cell 10 at time 14 = 45


Byte 7 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 7 at time 13 = 31

then value of cell 7 at time 14 = 31


Byte 12 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 12 at time 13 = 24

then value of cell 12 at time 14 = 24


Byte 13 Stays the Same 13
if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6
  • value of cell 13 at time 13 = 31

then value of cell 13 at time 14 = 31


Load 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 5 at time 14 = 10
  • value of cell 10 at time 14 = 45

then value of cell 7 at time 15 = 45


Pc 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0

then the PC at time 15 = 1


Byte 3 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 3 at time 14 = 3

then value of cell 3 at time 15 = 3


Byte 4 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 4 at time 14 = 2

then value of cell 4 at time 15 = 2


Byte 5 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 5 at time 14 = 10

then value of cell 5 at time 15 = 10


Byte 6 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 6 at time 14 = 14

then value of cell 6 at time 15 = 14


Byte 8 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 8 at time 14 = 24

then value of cell 8 at time 15 = 24


Byte 9 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 9 at time 14 = 31

then value of cell 9 at time 15 = 31


Byte 10 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 10 at time 14 = 45

then value of cell 10 at time 15 = 45


Byte 12 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 12 at time 14 = 24

then value of cell 12 at time 15 = 24


Byte 13 Stays the Same 14
if the following are true:
  • instruction #0 is load dst=7 addr=5 imm=0
  • the PC at time 14 = 0
  • value of cell 13 at time 14 = 31

then value of cell 13 at time 15 = 31


Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 6 at time 15 = 14
  • value of cell 7 at time 15 = 45

then value of cell 14 at time 16 = 45


Pc 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1

then the PC at time 16 = 2


Byte 3 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 3 at time 15 = 3
  • value of cell 6 at time 15 = 14

then value of cell 3 at time 16 = 3


Byte 4 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 4 at time 15 = 2
  • value of cell 6 at time 15 = 14

then value of cell 4 at time 16 = 2


Byte 5 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 5 at time 15 = 10
  • value of cell 6 at time 15 = 14

then value of cell 5 at time 16 = 10


Byte 6 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 6 at time 15 = 14
  • value of cell 6 at time 15 = 14

then value of cell 6 at time 16 = 14


Byte 8 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 8 at time 15 = 24
  • value of cell 6 at time 15 = 14

then value of cell 8 at time 16 = 24


Byte 9 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 9 at time 15 = 31
  • value of cell 6 at time 15 = 14

then value of cell 9 at time 16 = 31


Byte 10 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 10 at time 15 = 45
  • value of cell 6 at time 15 = 14

then value of cell 10 at time 16 = 45


Byte 7 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 7 at time 15 = 45
  • value of cell 6 at time 15 = 14

then value of cell 7 at time 16 = 45


Byte 12 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 12 at time 15 = 24
  • value of cell 6 at time 15 = 14

then value of cell 12 at time 16 = 24


Byte 13 Stays the Same Store 15
if the following are true:
  • instruction #1 is store src=7 addr=6 imm=0
  • the PC at time 15 = 1
  • value of cell 13 at time 15 = 31
  • value of cell 6 at time 15 = 14

then value of cell 13 at time 16 = 31


Addi Insn 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 5 at time 16 = 10

then value of cell 5 at time 17 = 11


Pc 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2

then the PC at time 17 = 3


Byte 3 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 3 at time 16 = 3

then value of cell 3 at time 17 = 3


Byte 4 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 4 at time 16 = 2

then value of cell 4 at time 17 = 2


Byte 6 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 6 at time 16 = 14

then value of cell 6 at time 17 = 14


Byte 8 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 8 at time 16 = 24

then value of cell 8 at time 17 = 24


Byte 9 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 9 at time 16 = 31

then value of cell 9 at time 17 = 31


Byte 10 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 10 at time 16 = 45

then value of cell 10 at time 17 = 45


Byte 7 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 7 at time 16 = 45

then value of cell 7 at time 17 = 45


Byte 12 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 12 at time 16 = 24

then value of cell 12 at time 17 = 24


Byte 13 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 13 at time 16 = 31

then value of cell 13 at time 17 = 31


Byte 14 Stays the Same 16
if the following are true:
  • instruction #2 is addi dst=5 src=5 imm=1
  • the PC at time 16 = 2
  • value of cell 14 at time 16 = 45

then value of cell 14 at time 17 = 45


Addi Insn 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 6 at time 17 = 14

then value of cell 6 at time 18 = 15


Pc 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3

then the PC at time 18 = 4


Byte 3 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 3 at time 17 = 3

then value of cell 3 at time 18 = 3


Byte 4 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 4 at time 17 = 2

then value of cell 4 at time 18 = 2


Byte 5 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 5 at time 17 = 11

then value of cell 5 at time 18 = 11


Byte 8 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 8 at time 17 = 24

then value of cell 8 at time 18 = 24


Byte 9 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 9 at time 17 = 31

then value of cell 9 at time 18 = 31


Byte 10 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 10 at time 17 = 45

then value of cell 10 at time 18 = 45


Byte 7 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 7 at time 17 = 45

then value of cell 7 at time 18 = 45


Byte 12 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 12 at time 17 = 24

then value of cell 12 at time 18 = 24


Byte 13 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 13 at time 17 = 31

then value of cell 13 at time 18 = 31


Byte 14 Stays the Same 17
if the following are true:
  • instruction #3 is addi dst=6 src=6 imm=1
  • the PC at time 17 = 3
  • value of cell 14 at time 17 = 45

then value of cell 14 at time 18 = 45


Addi Insn 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 4 at time 18 = 2

then value of cell 4 at time 19 = 3


Pc 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4

then the PC at time 19 = 5


Byte 3 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 3 at time 18 = 3

then value of cell 3 at time 19 = 3


Byte 5 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 5 at time 18 = 11

then value of cell 5 at time 19 = 11


Byte 6 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 6 at time 18 = 15

then value of cell 6 at time 19 = 15


Byte 8 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 8 at time 18 = 24

then value of cell 8 at time 19 = 24


Byte 9 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 9 at time 18 = 31

then value of cell 9 at time 19 = 31


Byte 10 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 10 at time 18 = 45

then value of cell 10 at time 19 = 45


Byte 7 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 7 at time 18 = 45

then value of cell 7 at time 19 = 45


Byte 12 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 12 at time 18 = 24

then value of cell 12 at time 19 = 24


Byte 13 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 13 at time 18 = 31

then value of cell 13 at time 19 = 31


Byte 14 Stays the Same 18
if the following are true:
  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 18 = 4
  • value of cell 14 at time 18 = 45

then value of cell 14 at time 19 = 45


Beq Branch
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 3 at time 19 = 3
  • value of cell 4 at time 19 = 3

then the PC at time 20 = 7


Byte 3 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 3 at time 19 = 3

then value of cell 3 at time 20 = 3


Byte 4 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 4 at time 19 = 3

then value of cell 4 at time 20 = 3


Byte 5 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 5 at time 19 = 11

then value of cell 5 at time 20 = 11


Byte 6 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 6 at time 19 = 15

then value of cell 6 at time 20 = 15


Byte 8 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 8 at time 19 = 24

then value of cell 8 at time 20 = 24


Byte 9 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 9 at time 19 = 31

then value of cell 9 at time 20 = 31


Byte 10 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 10 at time 19 = 45

then value of cell 10 at time 20 = 45


Byte 7 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 7 at time 19 = 45

then value of cell 7 at time 20 = 45


Byte 12 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 12 at time 19 = 24

then value of cell 12 at time 20 = 24


Byte 13 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 13 at time 19 = 31

then value of cell 13 at time 20 = 31


Byte 14 Stays the Same 19
if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 19 = 5
  • value of cell 14 at time 19 = 45

then value of cell 14 at time 20 = 45


Addi Zero Insn 0
if the following are true:
  • instruction #0 is addi dst=1 src=0 imm=128
  • the PC at time 0 = 0

then value of cell 1 at time 1 = 128



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