Proof: JAL Instruction Example

Let's prove the following theorem:

if the following are true:
  • instruction #5 is a JAL instruction with jump to: 1
  • the PC at time 2 = 5

then the PC at time 3 = 1

In this example, a JAL instruction causes the computer to jump to instruction #1.

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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Given
1 instruction #5 is a JAL instruction with jump to: 1
2 the PC at time 2 = 5
Proof Table
# Claim Reason
1 the PC at time (2 + 1) = 1 if instruction #5 is a JAL instruction with jump to: 1 and the PC at time 2 = 5, then the PC at time (2 + 1) = 1
2 2 + 1 = 3 2 + 1 = 3
3 the PC at time (2 + 1) = the PC at time 3 if 2 + 1 = 3, then the PC at time (2 + 1) = the PC at time 3
4 the PC at time 3 = 1 if the PC at time (2 + 1) = the PC at time 3 and the PC at time (2 + 1) = 1, then the PC at time 3 = 1

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