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 10 Stays the Same Store 1

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 1 = 1
value of cell 10 at time 1 = 45
value of cell 6 at time 1 = 12

then value of cell 10 at time 2 = 45

Byte 7 Stays the Same Store 1

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 1 = 1
value of cell 7 at time 1 = 24
value of cell 6 at time 1 = 12

then value of cell 7 at time 2 = 24

Addi Insn 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 5 at time 2 = 8

then value of cell 5 at time 3 = 9

Pc 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2

then the PC at time 3 = 3

Byte 3 Stays the Same 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 3 at time 2 = 3

then value of cell 3 at time 3 = 3

Byte 4 Stays the Same 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 4 at time 2 = 0

then value of cell 4 at time 3 = 0

Byte 6 Stays the Same 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 6 at time 2 = 12

then value of cell 6 at time 3 = 12

Byte 8 Stays the Same 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 8 at time 2 = 24

then value of cell 8 at time 3 = 24

Byte 9 Stays the Same 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 9 at time 2 = 31

then value of cell 9 at time 3 = 31

Byte 10 Stays the Same 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 10 at time 2 = 45

then value of cell 10 at time 3 = 45

Byte 7 Stays the Same 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 7 at time 2 = 24

then value of cell 7 at time 3 = 24

Byte 12 Stays the Same 2

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 2 = 2
value of cell 12 at time 2 = 24

then value of cell 12 at time 3 = 24

Addi Insn 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 6 at time 3 = 12

then value of cell 6 at time 4 = 13

Pc 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3

then the PC at time 4 = 4

Byte 3 Stays the Same 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 3 at time 3 = 3

then value of cell 3 at time 4 = 3

Byte 4 Stays the Same 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 4 at time 3 = 0

then value of cell 4 at time 4 = 0

Byte 5 Stays the Same 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 5 at time 3 = 9

then value of cell 5 at time 4 = 9

Byte 8 Stays the Same 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 8 at time 3 = 24

then value of cell 8 at time 4 = 24

Byte 9 Stays the Same 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 9 at time 3 = 31

then value of cell 9 at time 4 = 31

Byte 10 Stays the Same 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 10 at time 3 = 45

then value of cell 10 at time 4 = 45

Byte 7 Stays the Same 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 7 at time 3 = 24

then value of cell 7 at time 4 = 24

Byte 12 Stays the Same 3

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 12 at time 3 = 24

then value of cell 12 at time 4 = 24

Addi Insn 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 4 at time 4 = 0

then value of cell 4 at time 5 = 1

Pc 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4

then the PC at time 5 = 5

Byte 3 Stays the Same 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 3 at time 4 = 3

then value of cell 3 at time 5 = 3

Byte 5 Stays the Same 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 5 at time 4 = 9

then value of cell 5 at time 5 = 9

Byte 6 Stays the Same 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 6 at time 4 = 13

then value of cell 6 at time 5 = 13

Byte 8 Stays the Same 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 8 at time 4 = 24

then value of cell 8 at time 5 = 24

Byte 9 Stays the Same 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 9 at time 4 = 31

then value of cell 9 at time 5 = 31

Byte 10 Stays the Same 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 10 at time 4 = 45

then value of cell 10 at time 5 = 45

Byte 7 Stays the Same 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 7 at time 4 = 24

then value of cell 7 at time 5 = 24

Byte 12 Stays the Same 4

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 12 at time 4 = 24

then value of cell 12 at time 5 = 24

Beq No Branch 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 3 at time 5 = 3
value of cell 4 at time 5 = 1

then the PC at time 6 = 6

Byte 3 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 3 at time 5 = 3

then value of cell 3 at time 6 = 3

Byte 4 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 4 at time 5 = 1

then value of cell 4 at time 6 = 1

Byte 5 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 5 at time 5 = 9

then value of cell 5 at time 6 = 9

Byte 6 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 6 at time 5 = 13

then value of cell 6 at time 6 = 13

Byte 8 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 8 at time 5 = 24

then value of cell 8 at time 6 = 24

Byte 9 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 9 at time 5 = 31

then value of cell 9 at time 6 = 31

Byte 10 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 10 at time 5 = 45

then value of cell 10 at time 6 = 45

Byte 7 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 7 at time 5 = 24

then value of cell 7 at time 6 = 24

Byte 12 Stays the Same 5

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 5 = 5
value of cell 12 at time 5 = 24

then value of cell 12 at time 6 = 24

Jump Help 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6

then the PC at time 7 = 0

Byte 3 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 3 at time 6 = 3

then value of cell 3 at time 7 = 3

Byte 4 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 4 at time 6 = 1

then value of cell 4 at time 7 = 1

Byte 5 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 5 at time 6 = 9

then value of cell 5 at time 7 = 9

Byte 6 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 6 at time 6 = 13

then value of cell 6 at time 7 = 13

Byte 8 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 8 at time 6 = 24

then value of cell 8 at time 7 = 24

Byte 9 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 9 at time 6 = 31

then value of cell 9 at time 7 = 31

Byte 10 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 10 at time 6 = 45

then value of cell 10 at time 7 = 45

Byte 7 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 7 at time 6 = 24

then value of cell 7 at time 7 = 24

Byte 12 Stays the Same 6

if the following are true:

instruction #6 is jump imm=0
the PC at time 6 = 6
value of cell 12 at time 6 = 24

then value of cell 12 at time 7 = 24

Load 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 5 at time 7 = 9
value of cell 9 at time 7 = 31

then value of cell 7 at time 8 = 31

Pc 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0

then the PC at time 8 = 1

Byte 3 Stays the Same 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 3 at time 7 = 3

then value of cell 3 at time 8 = 3

Byte 4 Stays the Same 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 4 at time 7 = 1

then value of cell 4 at time 8 = 1

Byte 5 Stays the Same 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 5 at time 7 = 9

then value of cell 5 at time 8 = 9

Byte 6 Stays the Same 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 6 at time 7 = 13

then value of cell 6 at time 8 = 13

Byte 8 Stays the Same 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 8 at time 7 = 24

then value of cell 8 at time 8 = 24

Byte 9 Stays the Same 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 9 at time 7 = 31

then value of cell 9 at time 8 = 31

Byte 10 Stays the Same 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 10 at time 7 = 45

then value of cell 10 at time 8 = 45

Byte 12 Stays the Same 7

if the following are true:

instruction #0 is load dst=7 addr=5 imm=0
the PC at time 7 = 0
value of cell 12 at time 7 = 24

then value of cell 12 at time 8 = 24

Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 6 at time 8 = 13
value of cell 7 at time 8 = 31

then value of cell 13 at time 9 = 31

Pc 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1

then the PC at time 9 = 2

Byte 3 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 3 at time 8 = 3
value of cell 6 at time 8 = 13

then value of cell 3 at time 9 = 3

Byte 4 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 4 at time 8 = 1
value of cell 6 at time 8 = 13

then value of cell 4 at time 9 = 1

Byte 5 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 5 at time 8 = 9
value of cell 6 at time 8 = 13

then value of cell 5 at time 9 = 9

Byte 6 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 6 at time 8 = 13
value of cell 6 at time 8 = 13

then value of cell 6 at time 9 = 13

Byte 8 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 8 at time 8 = 24
value of cell 6 at time 8 = 13

then value of cell 8 at time 9 = 24

Byte 9 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 9 at time 8 = 31
value of cell 6 at time 8 = 13

then value of cell 9 at time 9 = 31

Byte 10 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 10 at time 8 = 45
value of cell 6 at time 8 = 13

then value of cell 10 at time 9 = 45

Byte 7 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 7 at time 8 = 31
value of cell 6 at time 8 = 13

then value of cell 7 at time 9 = 31

Byte 12 Stays the Same Store 8

if the following are true:

instruction #1 is store src=7 addr=6 imm=0
the PC at time 8 = 1
value of cell 12 at time 8 = 24
value of cell 6 at time 8 = 13

then value of cell 12 at time 9 = 24

Addi Insn 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 5 at time 9 = 9

then value of cell 5 at time 10 = 10

Pc 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2

then the PC at time 10 = 3

Byte 3 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 3 at time 9 = 3

then value of cell 3 at time 10 = 3

Byte 4 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 4 at time 9 = 1

then value of cell 4 at time 10 = 1

Byte 6 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 6 at time 9 = 13

then value of cell 6 at time 10 = 13

Byte 8 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 8 at time 9 = 24

then value of cell 8 at time 10 = 24

Byte 9 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 9 at time 9 = 31

then value of cell 9 at time 10 = 31

Byte 10 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 10 at time 9 = 45

then value of cell 10 at time 10 = 45

Byte 7 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 7 at time 9 = 31

then value of cell 7 at time 10 = 31

Byte 12 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 12 at time 9 = 24

then value of cell 12 at time 10 = 24

Byte 13 Stays the Same 9

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 13 at time 9 = 31

then value of cell 13 at time 10 = 31

Addi Insn 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 6 at time 10 = 13

then value of cell 6 at time 11 = 14

Pc 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3

then the PC at time 11 = 4

Byte 3 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 3 at time 10 = 3

then value of cell 3 at time 11 = 3

Byte 4 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 4 at time 10 = 1

then value of cell 4 at time 11 = 1

Byte 5 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 5 at time 10 = 10

then value of cell 5 at time 11 = 10

Byte 8 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 8 at time 10 = 24

then value of cell 8 at time 11 = 24

Byte 9 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 9 at time 10 = 31

then value of cell 9 at time 11 = 31

Byte 10 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 10 at time 10 = 45

then value of cell 10 at time 11 = 45

Byte 7 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 7 at time 10 = 31

then value of cell 7 at time 11 = 31

Byte 12 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 12 at time 10 = 24

then value of cell 12 at time 11 = 24

Byte 13 Stays the Same 10

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 13 at time 10 = 31

then value of cell 13 at time 11 = 31

Addi Insn 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 4 at time 11 = 1

then value of cell 4 at time 12 = 2

Pc 11

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 11 = 4

then the PC at time 12 = 5

Byte 3 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 3 at time 11 = 3

then value of cell 3 at time 12 = 3

Byte 5 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 5 at time 11 = 10

then value of cell 5 at time 12 = 10

Byte 6 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 6 at time 11 = 14

then value of cell 6 at time 12 = 14

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