Proof: JAL Instruction Store 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 value of cell 2 at time 3 = 6

In this example, the JAL instruction causes the computer to store the current PC value + 1 in memory cell #2.

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 value of cell 2 at time (2 + 1) = 5 + 1 if instruction #5 is a JAL instruction with jump to: 1 and the PC at time 2 = 5, then value of cell 2 at time (2 + 1) = 5 + 1
2 5 + 1 = 6 5 + 1 = 6
3 2 + 1 = 3 2 + 1 = 3
4 value of cell 2 at time (2 + 1) = value of cell 2 at time 3 if 2 + 1 = 3, then value of cell 2 at time (2 + 1) = value of cell 2 at time 3
5 value of cell 2 at time (2 + 1) = 6 if value of cell 2 at time (2 + 1) = 5 + 1 and 5 + 1 = 6, then value of cell 2 at time (2 + 1) = 6
6 value of cell 2 at time 3 = 6 if value of cell 2 at time (2 + 1) = value of cell 2 at time 3 and value of cell 2 at time (2 + 1) = 6, then value of cell 2 at time 3 = 6

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