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

Addi Insn 6

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 6 = 6
value of cell 3 at time 6 = 1

then value of cell 2 at time 7 = 1

Pc 6

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 6 = 6

then the PC at time 7 = 7

Byte 1 Stays the Same 6

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 6 = 6
value of cell 1 at time 6 = 1

then value of cell 1 at time 7 = 1

Byte 4 Stays the Same 6

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 6 = 6
value of cell 4 at time 6 = 0

then value of cell 4 at time 7 = 0

Byte 5 Stays the Same 6

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 6 = 6
value of cell 5 at time 6 = 4

then value of cell 5 at time 7 = 4

Byte 3 Stays the Same 6

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 6 = 6
value of cell 3 at time 6 = 1

then value of cell 3 at time 7 = 1

Addi Insn 7

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 7 = 7
value of cell 4 at time 7 = 0

then value of cell 4 at time 8 = 1

Pc 7

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 7 = 7

then the PC at time 8 = 8

Byte 1 Stays the Same 7

if the following are true:

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

then value of cell 1 at time 8 = 1

Byte 2 Stays the Same 7

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 7 = 7
value of cell 2 at time 7 = 1

then value of cell 2 at time 8 = 1

Byte 5 Stays the Same 7

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 7 = 7
value of cell 5 at time 7 = 4

then value of cell 5 at time 8 = 4

Byte 3 Stays the Same 7

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 7 = 7
value of cell 3 at time 7 = 1

then value of cell 3 at time 8 = 1

Beq No Branch 8

if the following are true:

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

then the PC at time 9 = 9

Byte 1 Stays the Same 8

if the following are true:

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

then value of cell 1 at time 9 = 1

Byte 2 Stays the Same 8

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 8 = 8
value of cell 2 at time 8 = 1

then value of cell 2 at time 9 = 1

Byte 4 Stays the Same 8

if the following are true:

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

then value of cell 4 at time 9 = 1

Byte 5 Stays the Same 8

if the following are true:

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

then value of cell 5 at time 9 = 4

Byte 3 Stays the Same 8

if the following are true:

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

then value of cell 3 at time 9 = 1

Jump Help 9

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 9 = 9

then the PC at time 10 = 4

Byte 1 Stays the Same 9

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 9 = 9
value of cell 1 at time 9 = 1

then value of cell 1 at time 10 = 1

Byte 2 Stays the Same 9

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 9 = 9
value of cell 2 at time 9 = 1

then value of cell 2 at time 10 = 1

Byte 4 Stays the Same 9

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 9 = 9
value of cell 4 at time 9 = 1

then value of cell 4 at time 10 = 1

Byte 5 Stays the Same 9

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 9 = 9
value of cell 5 at time 9 = 4

then value of cell 5 at time 10 = 4

Byte 3 Stays the Same 9

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 9 = 9
value of cell 3 at time 9 = 1

then value of cell 3 at time 10 = 1

Add Insn 10

if the following are true:

the PC at time 10 = 4
instruction #4 is add dst=3 src1=1 src2=2

then value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10)

Substitute Add 10

if the following are true:

value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10)
value of cell 1 at time 10 = 1
value of cell 2 at time 10 = 1

then value of cell 3 at time 11 = 2

Pc 10

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 10 = 4

then the PC at time 11 = 5

Byte 1 Stays the Same 10

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 10 = 4
value of cell 1 at time 10 = 1

then value of cell 1 at time 11 = 1

Byte 2 Stays the Same 10

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 10 = 4
value of cell 2 at time 10 = 1

then value of cell 2 at time 11 = 1

Byte 4 Stays the Same 10

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 10 = 4
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 #4 is add dst=3 src1=1 src2=2
the PC at time 10 = 4
value of cell 5 at time 10 = 4

then value of cell 5 at time 11 = 4

Addi Insn 11

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 11 = 5
value of cell 2 at time 11 = 1

then value of cell 1 at time 12 = 1

Pc 11

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 11 = 5

then the PC at time 12 = 6

Byte 2 Stays the Same 11

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 11 = 5
value of cell 2 at time 11 = 1

then value of cell 2 at time 12 = 1

Byte 4 Stays the Same 11

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 11 = 5
value of cell 4 at time 11 = 1

then value of cell 4 at time 12 = 1

Byte 5 Stays the Same 11

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 11 = 5
value of cell 5 at time 11 = 4

then value of cell 5 at time 12 = 4

Byte 3 Stays the Same 11

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 11 = 5
value of cell 3 at time 11 = 2

then value of cell 3 at time 12 = 2

Addi Insn 12

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 12 = 6
value of cell 3 at time 12 = 2

then value of cell 2 at time 13 = 2

Pc 12

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 12 = 6

then the PC at time 13 = 7

Byte 1 Stays the Same 12

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 12 = 6
value of cell 1 at time 12 = 1

then value of cell 1 at time 13 = 1

Byte 4 Stays the Same 12

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 12 = 6
value of cell 4 at time 12 = 1

then value of cell 4 at time 13 = 1

Byte 5 Stays the Same 12

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 12 = 6
value of cell 5 at time 12 = 4

then value of cell 5 at time 13 = 4

Byte 3 Stays the Same 12

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 12 = 6
value of cell 3 at time 12 = 2

then value of cell 3 at time 13 = 2

Addi Insn 13

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 13 = 7
value of cell 4 at time 13 = 1

then value of cell 4 at time 14 = 2

Pc 13

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 13 = 7

then the PC at time 14 = 8

Byte 1 Stays the Same 13

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 13 = 7
value of cell 1 at time 13 = 1

then value of cell 1 at time 14 = 1

Byte 2 Stays the Same 13

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 13 = 7
value of cell 2 at time 13 = 2

then value of cell 2 at time 14 = 2

Byte 5 Stays the Same 13

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 13 = 7
value of cell 5 at time 13 = 4

then value of cell 5 at time 14 = 4

Byte 3 Stays the Same 13

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 13 = 7
value of cell 3 at time 13 = 2

then value of cell 3 at time 14 = 2

Beq No Branch 14

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 14 = 8
value of cell 4 at time 14 = 2
value of cell 5 at time 14 = 4

then the PC at time 15 = 9

Byte 1 Stays the Same 14

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 14 = 8
value of cell 1 at time 14 = 1

then value of cell 1 at time 15 = 1

Byte 2 Stays the Same 14

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 14 = 8
value of cell 2 at time 14 = 2

then value of cell 2 at time 15 = 2

Byte 4 Stays the Same 14

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 14 = 8
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 #8 is beq left=4 right=5 imm=1
the PC at time 14 = 8
value of cell 5 at time 14 = 4

then value of cell 5 at time 15 = 4

Byte 3 Stays the Same 14

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 14 = 8
value of cell 3 at time 14 = 2

then value of cell 3 at time 15 = 2

Jump Help 15

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 15 = 9

then the PC at time 16 = 4

Byte 1 Stays the Same 15

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 15 = 9
value of cell 1 at time 15 = 1

then value of cell 1 at time 16 = 1

Byte 2 Stays the Same 15

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 15 = 9
value of cell 2 at time 15 = 2

then value of cell 2 at time 16 = 2

Byte 4 Stays the Same 15

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 15 = 9
value of cell 4 at time 15 = 2

then value of cell 4 at time 16 = 2

Byte 5 Stays the Same 15

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 15 = 9
value of cell 5 at time 15 = 4

then value of cell 5 at time 16 = 4

Byte 3 Stays the Same 15

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 15 = 9
value of cell 3 at time 15 = 2

then value of cell 3 at time 16 = 2

Add Insn 16

if the following are true:

the PC at time 16 = 4
instruction #4 is add dst=3 src1=1 src2=2

then value of cell 3 at time 17 = (value of cell 1 at time 16) + (value of cell 2 at time 16)

Substitute Add 16

if the following are true:

value of cell 3 at time 17 = (value of cell 1 at time 16) + (value of cell 2 at time 16)
value of cell 1 at time 16 = 1
value of cell 2 at time 16 = 2

then value of cell 3 at time 17 = 3

Pc 16

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 16 = 4

then the PC at time 17 = 5

Byte 1 Stays the Same 16

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 16 = 4
value of cell 1 at time 16 = 1

then value of cell 1 at time 17 = 1

Byte 2 Stays the Same 16

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 16 = 4
value of cell 2 at time 16 = 2

then value of cell 2 at time 17 = 2

Byte 4 Stays the Same 16

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 16 = 4
value of cell 4 at time 16 = 2

then value of cell 4 at time 17 = 2

Byte 5 Stays the Same 16

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 16 = 4
value of cell 5 at time 16 = 4

then value of cell 5 at time 17 = 4

Addi Insn 17

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 17 = 5
value of cell 2 at time 17 = 2

then value of cell 1 at time 18 = 2

Pc 17

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 17 = 5

then the PC at time 18 = 6

Byte 2 Stays the Same 17

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 17 = 5
value of cell 2 at time 17 = 2

then value of cell 2 at time 18 = 2

Byte 4 Stays the Same 17

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 17 = 5
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 #5 is addi dst=1 src=2 imm=0
the PC at time 17 = 5
value of cell 5 at time 17 = 4

then value of cell 5 at time 18 = 4

Byte 3 Stays the Same 17

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 17 = 5
value of cell 3 at time 17 = 3

then value of cell 3 at time 18 = 3

Addi Insn 18

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 18 = 6
value of cell 3 at time 18 = 3

then value of cell 2 at time 19 = 3

Pc 18

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 18 = 6

then the PC at time 19 = 7

Byte 1 Stays the Same 18

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 18 = 6
value of cell 1 at time 18 = 2

then value of cell 1 at time 19 = 2

Byte 4 Stays the Same 18

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 18 = 6
value of cell 4 at time 18 = 2

then value of cell 4 at time 19 = 2

Byte 5 Stays the Same 18

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 18 = 6
value of cell 5 at time 18 = 4

then value of cell 5 at time 19 = 4

Byte 3 Stays the Same 18

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 18 = 6
value of cell 3 at time 18 = 3

then value of cell 3 at time 19 = 3

Addi Insn 19

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 19 = 7
value of cell 4 at time 19 = 2

then value of cell 4 at time 20 = 3

Pc 19

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 19 = 7

then the PC at time 20 = 8

Byte 1 Stays the Same 19

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 19 = 7
value of cell 1 at time 19 = 2

then value of cell 1 at time 20 = 2

Byte 2 Stays the Same 19

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 19 = 7
value of cell 2 at time 19 = 3

then value of cell 2 at time 20 = 3

Byte 5 Stays the Same 19

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 19 = 7
value of cell 5 at time 19 = 4

then value of cell 5 at time 20 = 4

Byte 3 Stays the Same 19

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 19 = 7
value of cell 3 at time 19 = 3

then value of cell 3 at time 20 = 3

Beq No Branch 20

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 20 = 8
value of cell 4 at time 20 = 3
value of cell 5 at time 20 = 4

then the PC at time 21 = 9

Byte 1 Stays the Same 20

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 20 = 8
value of cell 1 at time 20 = 2

then value of cell 1 at time 21 = 2

Byte 2 Stays the Same 20

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 20 = 8
value of cell 2 at time 20 = 3

then value of cell 2 at time 21 = 3

Byte 4 Stays the Same 20

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 20 = 8
value of cell 4 at time 20 = 3

then value of cell 4 at time 21 = 3

Byte 5 Stays the Same 20

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 20 = 8
value of cell 5 at time 20 = 4

then value of cell 5 at time 21 = 4

Byte 3 Stays the Same 20

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 20 = 8
value of cell 3 at time 20 = 3

then value of cell 3 at time 21 = 3

Jump Help 21

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 21 = 9

then the PC at time 22 = 4

Byte 1 Stays the Same 21

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 21 = 9
value of cell 1 at time 21 = 2

then value of cell 1 at time 22 = 2

Byte 2 Stays the Same 21

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 21 = 9
value of cell 2 at time 21 = 3

then value of cell 2 at time 22 = 3

Byte 4 Stays the Same 21

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 21 = 9
value of cell 4 at time 21 = 3

then value of cell 4 at time 22 = 3

Byte 5 Stays the Same 21

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 21 = 9
value of cell 5 at time 21 = 4

then value of cell 5 at time 22 = 4

Byte 3 Stays the Same 21

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 21 = 9
value of cell 3 at time 21 = 3

then value of cell 3 at time 22 = 3

Add Insn 22

if the following are true:

the PC at time 22 = 4
instruction #4 is add dst=3 src1=1 src2=2

then value of cell 3 at time 23 = (value of cell 1 at time 22) + (value of cell 2 at time 22)

Substitute Add 22

if the following are true:

value of cell 3 at time 23 = (value of cell 1 at time 22) + (value of cell 2 at time 22)
value of cell 1 at time 22 = 2
value of cell 2 at time 22 = 3

then value of cell 3 at time 23 = 5

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