Proof: Addi Insn 22

Let's prove the following theorem:

if the following are true:

instruction #22 is addi dst=1 src=1 imm=3
the PC at time 22 = 22
value of cell 1 at time 22 = 123

then value of cell 1 at time 23 = 126

Proof:

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Given

1	instruction #22 is `addi dst=1 src=1 imm=3`
2	the PC at time 22 = 22
3	value of cell 1 at time 22 = 123

Proof Table

#	Claim	Reason
1	value of cell 1 at time (22 + 1) = (value of cell 1 at time 22) + 3	if instruction #22 is `addi dst=1 src=1 imm=3` and the PC at time 22 = 22, then value of cell 1 at time (22 + 1) = (value of cell 1 at time 22) + 3 (ADDI Instruction Property)
2	22 + 1 = 23	22 + 1 = 23 (Fixed Value Statement)
3	value of cell 1 at time (22 + 1) = value of cell 1 at time 23	if 22 + 1 = 23, then value of cell 1 at time (22 + 1) = value of cell 1 at time 23 (Substitution)
4	value of cell 1 at time 23 = (value of cell 1 at time 22) + 3	if value of cell 1 at time (22 + 1) = value of cell 1 at time 23 and value of cell 1 at time (22 + 1) = (value of cell 1 at time 22) + 3, then value of cell 1 at time 23 = (value of cell 1 at time 22) + 3 (Transitive Property of Equality Variation 2)
5	value of cell 1 at time 23 = 123 + 3	if value of cell 1 at time 23 = (value of cell 1 at time 22) + 3 and value of cell 1 at time 22 = 123, then value of cell 1 at time 23 = 123 + 3 (Term 1 Substitution)
6	123 + 3 = 126	123 + 3 = 126 (Fixed Value Statement)
7	value of cell 1 at time 23 = 126	if value of cell 1 at time 23 = 123 + 3 and 123 + 3 = 126, then value of cell 1 at time 23 = 126 (Transitive Property of Equality)

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