Proof: Add Insn 4

Let's prove the following theorem:

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

then value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4)

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 the PC at time 4 = 4
2 instruction #4 is add dst=3 src1=1 src2=2
Proof Table
# Claim Reason
1 value of cell 3 at time (4 + 1) = (value of cell 1 at time 4) + (value of cell 2 at time 4) if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 4 = 4, then value of cell 3 at time (4 + 1) = (value of cell 1 at time 4) + (value of cell 2 at time 4)
2 4 + 1 = 5 4 + 1 = 5
3 value of cell 3 at time (4 + 1) = value of cell 3 at time 5 if 4 + 1 = 5, then value of cell 3 at time (4 + 1) = value of cell 3 at time 5
4 value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4) if value of cell 3 at time (4 + 1) = value of cell 3 at time 5 and value of cell 3 at time (4 + 1) = (value of cell 1 at time 4) + (value of cell 2 at time 4), then value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4)

Comments

Please log in to add comments