Proof: Addi Insn 18

Let's prove the following theorem:

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 18 = 6
value of cell 3 at time 18 = 3

then value of cell 2 at time 19 = 3

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #6 is `addi dst=2 src=3 imm=0`
2	the PC at time 18 = 6
3	value of cell 3 at time 18 = 3

Proof Table

#	Claim	Reason
1	value of cell 2 at time (18 + 1) = (value of cell 3 at time 18) + 0	if instruction #6 is `addi dst=2 src=3 imm=0` and the PC at time 18 = 6, then value of cell 2 at time (18 + 1) = (value of cell 3 at time 18) + 0 (ADDI Instruction Property)
2	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
3	value of cell 2 at time (18 + 1) = value of cell 2 at time 19	if 18 + 1 = 19, then value of cell 2 at time (18 + 1) = value of cell 2 at time 19 (Substitution)
4	value of cell 2 at time 19 = (value of cell 3 at time 18) + 0	if value of cell 2 at time (18 + 1) = value of cell 2 at time 19 and value of cell 2 at time (18 + 1) = (value of cell 3 at time 18) + 0, then value of cell 2 at time 19 = (value of cell 3 at time 18) + 0 (Transitive Property of Equality Variation 2)
5	value of cell 2 at time 19 = 3 + 0	if value of cell 2 at time 19 = (value of cell 3 at time 18) + 0 and value of cell 3 at time 18 = 3, then value of cell 2 at time 19 = 3 + 0 (Term 1 Substitution)
6	3 + 0 = 3	3 + 0 = 3 (Additive Identity)
7	value of cell 2 at time 19 = 3	if value of cell 2 at time 19 = 3 + 0 and 3 + 0 = 3, then value of cell 2 at time 19 = 3 (Transitive Property of Equality)

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