Proof: JAL Instruction Example 3

Let's prove the following theorem:

if the following are true:
  • instruction #i is a JAL instruction with jump to: 1
  • the PC at time 2 = i
  • not (x = 2)

then value of cell x at time 3 = value of cell x at time 2

In this example, the JAL instruction does not change memory cell values.

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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Given
1 instruction #i is a JAL instruction with jump to: 1
2 the PC at time 2 = i
3 not (x = 2)
Proof Table
# Claim Reason
1 value of cell x at time (2 + 1) = value of cell x at time 2 if instruction #i is a JAL instruction with jump to: 1 and the PC at time 2 = i and not (x = 2), then value of cell x at time (2 + 1) = value of cell x at time 2
2 2 + 1 = 3 2 + 1 = 3
3 value of cell x at time (2 + 1) = value of cell x at time 3 if 2 + 1 = 3, then value of cell x at time (2 + 1) = value of cell x at time 3
4 value of cell x at time 3 = value of cell x at time 2 if value of cell x at time (2 + 1) = value of cell x at time 3 and value of cell x at time (2 + 1) = value of cell x at time 2, then value of cell x at time 3 = value of cell x at time 2

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