Proof: Byte 5 Stays the Same 16

Let's prove the following theorem:

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

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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Given
1 instruction #4 is add dst=3 src1=1 src2=2
2 the PC at time 16 = 4
3 value of cell 5 at time 16 = 4
Proof Table
# Claim Reason
1 not (5 = 3) not (5 = 3)
2 value of cell 5 at time (16 + 1) = value of cell 5 at time 16 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 16 = 4 and not (5 = 3), then value of cell 5 at time (16 + 1) = value of cell 5 at time 16
3 16 + 1 = 17 16 + 1 = 17
4 value of cell 5 at time (16 + 1) = value of cell 5 at time 17 if 16 + 1 = 17, then value of cell 5 at time (16 + 1) = value of cell 5 at time 17
5 value of cell 5 at time 17 = value of cell 5 at time 16 if value of cell 5 at time (16 + 1) = value of cell 5 at time 17 and value of cell 5 at time (16 + 1) = value of cell 5 at time 16, then value of cell 5 at time 17 = value of cell 5 at time 16
6 value of cell 5 at time 17 = 4 if value of cell 5 at time 17 = value of cell 5 at time 16 and value of cell 5 at time 16 = 4, then value of cell 5 at time 17 = 4

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