Proof: Addi Insn 1

Let's prove the following theorem:

if the following are true:

instruction #1 is addi dst=8 src=4 imm=0
the PC at time 1 = 1
value of cell 4 at time 1 = 11

then value of cell 8 at time 2 = 11

Proof:

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Given

1	instruction #1 is `addi dst=8 src=4 imm=0`
2	the PC at time 1 = 1
3	value of cell 4 at time 1 = 11

Proof Table

#	Claim	Reason
1	value of cell 8 at time (1 + 1) = (value of cell 4 at time 1) + 0	if instruction #1 is `addi dst=8 src=4 imm=0` and the PC at time 1 = 1, then value of cell 8 at time (1 + 1) = (value of cell 4 at time 1) + 0 (ADDI Instruction Property)
2	1 + 1 = 2	1 + 1 = 2 (Fixed Value Statement)
3	value of cell 8 at time (1 + 1) = value of cell 8 at time 2	if 1 + 1 = 2, then value of cell 8 at time (1 + 1) = value of cell 8 at time 2 (Substitution)
4	value of cell 8 at time 2 = (value of cell 4 at time 1) + 0	if value of cell 8 at time (1 + 1) = value of cell 8 at time 2 and value of cell 8 at time (1 + 1) = (value of cell 4 at time 1) + 0, then value of cell 8 at time 2 = (value of cell 4 at time 1) + 0 (Transitive Property of Equality Variation 2)
5	value of cell 8 at time 2 = 11 + 0	if value of cell 8 at time 2 = (value of cell 4 at time 1) + 0 and value of cell 4 at time 1 = 11, then value of cell 8 at time 2 = 11 + 0 (Term 1 Substitution)
6	11 + 0 = 11	11 + 0 = 11 (Additive Identity)
7	value of cell 8 at time 2 = 11	if value of cell 8 at time 2 = 11 + 0 and 11 + 0 = 11, then value of cell 8 at time 2 = 11 (Transitive Property of Equality)

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