Proof: Byte 5 Stays the Same 6

Let's prove the following theorem:

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

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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

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