Proof: JUMP Instruction Example 2

Let's prove the following theorem:

if the following are true:
  • instruction #0 is jump imm=jump_to
  • the PC at time 0 = 0

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

This example shows that a JUMP instruction does not change memory cell values. With some algebra, we prove that any memory cell at time 1 is equal to the cell at time 0.

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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Given
1 instruction #0 is jump imm=jump_to
2 the PC at time 0 = 0
Proof Table
# Claim Reason
1 value of cell x at time (0 + 1) = value of cell x at time 0 if instruction #0 is jump imm=jump_to and the PC at time 0 = 0, then value of cell x at time (0 + 1) = value of cell x at time 0
2 0 + 1 = 1 0 + 1 = 1
3 value of cell x at time (0 + 1) = value of cell x at time 1 if 0 + 1 = 1, then value of cell x at time (0 + 1) = value of cell x at time 1
4 value of cell x at time 1 = value of cell x at time 0 if value of cell x at time (0 + 1) = value of cell x at time 1 and value of cell x at time (0 + 1) = value of cell x at time 0, then value of cell x at time 1 = value of cell x at time 0

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