Proof: Add Insn 22

Let's prove the following theorem:

if the following are true:

the PC at time 22 = 4
instruction #4 is add dst=3 src1=1 src2=2

then value of cell 3 at time 23 = (value of cell 1 at time 22) + (value of cell 2 at time 22)

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	the PC at time 22 = 4
2	instruction #4 is `add dst=3 src1=1 src2=2`

Proof Table

#	Claim	Reason
1	value of cell 3 at time (22 + 1) = (value of cell 1 at time 22) + (value of cell 2 at time 22)	if instruction #4 is `add dst=3 src1=1 src2=2` and the PC at time 22 = 4, then value of cell 3 at time (22 + 1) = (value of cell 1 at time 22) + (value of cell 2 at time 22) (ADD Instruction Property)
2	22 + 1 = 23	22 + 1 = 23 (Fixed Value Statement)
3	value of cell 3 at time (22 + 1) = value of cell 3 at time 23	if 22 + 1 = 23, then value of cell 3 at time (22 + 1) = value of cell 3 at time 23 (Substitution)
4	value of cell 3 at time 23 = (value of cell 1 at time 22) + (value of cell 2 at time 22)	if value of cell 3 at time (22 + 1) = value of cell 3 at time 23 and value of cell 3 at time (22 + 1) = (value of cell 1 at time 22) + (value of cell 2 at time 22), then value of cell 3 at time 23 = (value of cell 1 at time 22) + (value of cell 2 at time 22) (Transitive Property of Equality Variation 2)

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