Proof: LOAD Instruction Example 3

Let's prove the following theorem:

if the following are true:
  • instruction #0 is load dst=5 addr=1 imm=1
  • the PC at time 0 = 0

then value of cell 2 at time 1 = value of cell 2 at time 0

The following example shows that when a LOAD instruction with dst = 5 is executed, memory cell #2 stays unchanged.

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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

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