Proof: Addi Insn 17

Let's prove the following theorem:

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 17 = 5
value of cell 2 at time 17 = 2

then value of cell 1 at time 18 = 2

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #5 is `addi dst=1 src=2 imm=0`
2	the PC at time 17 = 5
3	value of cell 2 at time 17 = 2

Proof Table

#	Claim	Reason
1	value of cell 1 at time (17 + 1) = (value of cell 2 at time 17) + 0	if instruction #5 is `addi dst=1 src=2 imm=0` and the PC at time 17 = 5, then value of cell 1 at time (17 + 1) = (value of cell 2 at time 17) + 0 (ADDI Instruction Property)
2	17 + 1 = 18	17 + 1 = 18 (Fixed Value Statement)
3	value of cell 1 at time (17 + 1) = value of cell 1 at time 18	if 17 + 1 = 18, then value of cell 1 at time (17 + 1) = value of cell 1 at time 18 (Substitution)
4	value of cell 1 at time 18 = (value of cell 2 at time 17) + 0	if value of cell 1 at time (17 + 1) = value of cell 1 at time 18 and value of cell 1 at time (17 + 1) = (value of cell 2 at time 17) + 0, then value of cell 1 at time 18 = (value of cell 2 at time 17) + 0 (Transitive Property of Equality Variation 2)
5	value of cell 1 at time 18 = 2 + 0	if value of cell 1 at time 18 = (value of cell 2 at time 17) + 0 and value of cell 2 at time 17 = 2, then value of cell 1 at time 18 = 2 + 0 (Term 1 Substitution)
6	2 + 0 = 2	2 + 0 = 2 (Additive Identity)
7	value of cell 1 at time 18 = 2	if value of cell 1 at time 18 = 2 + 0 and 2 + 0 = 2, then value of cell 1 at time 18 = 2 (Transitive Property of Equality)

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