Proof: Byte 3 Stays the Same 0

Let's prove the following theorem:

if the following are true:
  • instruction #0 is addi dst=7 src=3 imm=0
  • the PC at time 0 = 0
  • value of cell 3 at time 0 = 13

then value of cell 3 at time 1 = 13

Proof:

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Given
1 instruction #0 is addi dst=7 src=3 imm=0
2 the PC at time 0 = 0
3 value of cell 3 at time 0 = 13
Proof Table
# Claim Reason
1 not (3 = 7) not (3 = 7)
2 value of cell 3 at time (0 + 1) = value of cell 3 at time 0 if instruction #0 is addi dst=7 src=3 imm=0 and the PC at time 0 = 0 and not (3 = 7), then value of cell 3 at time (0 + 1) = value of cell 3 at time 0
3 0 + 1 = 1 0 + 1 = 1
4 value of cell 3 at time (0 + 1) = value of cell 3 at time 1 if 0 + 1 = 1, then value of cell 3 at time (0 + 1) = value of cell 3 at time 1
5 value of cell 3 at time 1 = value of cell 3 at time 0 if value of cell 3 at time (0 + 1) = value of cell 3 at time 1 and value of cell 3 at time (0 + 1) = value of cell 3 at time 0, then value of cell 3 at time 1 = value of cell 3 at time 0
6 value of cell 3 at time 1 = 13 if value of cell 3 at time 1 = value of cell 3 at time 0 and value of cell 3 at time 0 = 13, then value of cell 3 at time 1 = 13

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