Proof: JUMPR Instruction Example

Let's prove the following theorem:

if the following are true:
  • instruction #0 is jumpr addr=1
  • the PC at time 0 = 0
  • value of cell 1 at time 0 = 3

then the PC at time 1 = 3

In this example, a JUMPR instruction causes the computer to jump to the value in memory cell #1.

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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

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