Proof: Byte 127 Stays the Same 17

Let's prove the following theorem:

if the following are true:
  • instruction #4 is add dst=3 src1=3 src2=4
  • the PC at time 17 = 4
  • value of cell 127 at time 17 = 2

then value of cell 127 at time 18 = 2

Proof:

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Given
1 instruction #4 is add dst=3 src1=3 src2=4
2 the PC at time 17 = 4
3 value of cell 127 at time 17 = 2
Proof Table
# Claim Reason
1 not (127 = 3) not (127 = 3)
2 value of cell 127 at time (17 + 1) = value of cell 127 at time 17 if instruction #4 is add dst=3 src1=3 src2=4 and the PC at time 17 = 4 and not (127 = 3), then value of cell 127 at time (17 + 1) = value of cell 127 at time 17
3 17 + 1 = 18 17 + 1 = 18
4 value of cell 127 at time (17 + 1) = value of cell 127 at time 18 if 17 + 1 = 18, then value of cell 127 at time (17 + 1) = value of cell 127 at time 18
5 value of cell 127 at time 18 = value of cell 127 at time 17 if value of cell 127 at time (17 + 1) = value of cell 127 at time 18 and value of cell 127 at time (17 + 1) = value of cell 127 at time 17, then value of cell 127 at time 18 = value of cell 127 at time 17
6 value of cell 127 at time 18 = 2 if value of cell 127 at time 18 = value of cell 127 at time 17 and value of cell 127 at time 17 = 2, then value of cell 127 at time 18 = 2

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