Proof: Byte 5 Stays the Same 21

Let's prove the following theorem:

if the following are true:
  • instruction #9 is jump imm=(-6)
  • the PC at time 21 = 9
  • value of cell 5 at time 21 = 4

then value of cell 5 at time 22 = 4

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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Given
1 instruction #9 is jump imm=(-6)
2 the PC at time 21 = 9
3 value of cell 5 at time 21 = 4
Proof Table
# Claim Reason
1 value of cell 5 at time (21 + 1) = value of cell 5 at time 21 if instruction #9 is jump imm=(-6) and the PC at time 21 = 9, then value of cell 5 at time (21 + 1) = value of cell 5 at time 21
2 21 + 1 = 22 21 + 1 = 22
3 value of cell 5 at time (21 + 1) = value of cell 5 at time 22 if 21 + 1 = 22, then value of cell 5 at time (21 + 1) = value of cell 5 at time 22
4 value of cell 5 at time 22 = value of cell 5 at time 21 if value of cell 5 at time (21 + 1) = value of cell 5 at time 22 and value of cell 5 at time (21 + 1) = value of cell 5 at time 21, then value of cell 5 at time 22 = value of cell 5 at time 21
5 value of cell 5 at time 22 = 4 if value of cell 5 at time 22 = value of cell 5 at time 21 and value of cell 5 at time 21 = 4, then value of cell 5 at time 22 = 4

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