Proof: Byte 127 Stays the Same 15

Let's prove the following theorem:

if the following are true:
  • instruction #2 is load dst=3 addr=1 imm=1
  • the PC at time 15 = 2
  • value of cell 127 at time 15 = 2

then value of cell 127 at time 16 = 2

Proof:

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Given
1 instruction #2 is load dst=3 addr=1 imm=1
2 the PC at time 15 = 2
3 value of cell 127 at time 15 = 2
Proof Table
# Claim Reason
1 not (127 = 3) not (127 = 3)
2 value of cell 127 at time (15 + 1) = value of cell 127 at time 15 if instruction #2 is load dst=3 addr=1 imm=1 and the PC at time 15 = 2 and not (127 = 3), then value of cell 127 at time (15 + 1) = value of cell 127 at time 15
3 15 + 1 = 16 15 + 1 = 16
4 value of cell 127 at time (15 + 1) = value of cell 127 at time 16 if 15 + 1 = 16, then value of cell 127 at time (15 + 1) = value of cell 127 at time 16
5 value of cell 127 at time 16 = value of cell 127 at time 15 if value of cell 127 at time (15 + 1) = value of cell 127 at time 16 and value of cell 127 at time (15 + 1) = value of cell 127 at time 15, then value of cell 127 at time 16 = value of cell 127 at time 15
6 value of cell 127 at time 16 = 2 if value of cell 127 at time 16 = value of cell 127 at time 15 and value of cell 127 at time 15 = 2, then value of cell 127 at time 16 = 2

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