Proof: Add Insn 10

Let's prove the following theorem:

if the following are true:
  • the PC at time 10 = 4
  • instruction #4 is add dst=3 src1=1 src2=2

then value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10)

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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Given
1 the PC at time 10 = 4
2 instruction #4 is add dst=3 src1=1 src2=2
Proof Table
# Claim Reason
1 value of cell 3 at time (10 + 1) = (value of cell 1 at time 10) + (value of cell 2 at time 10) if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 10 = 4, then value of cell 3 at time (10 + 1) = (value of cell 1 at time 10) + (value of cell 2 at time 10)
2 10 + 1 = 11 10 + 1 = 11
3 value of cell 3 at time (10 + 1) = value of cell 3 at time 11 if 10 + 1 = 11, then value of cell 3 at time (10 + 1) = value of cell 3 at time 11
4 value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10) if value of cell 3 at time (10 + 1) = value of cell 3 at time 11 and value of cell 3 at time (10 + 1) = (value of cell 1 at time 10) + (value of cell 2 at time 10), then value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10)

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