Proof: Addi Insn 7

Let's prove the following theorem:

if the following are true:

instruction #3 is addi dst=5 src=5 imm=7
the PC at time 7 = 3
value of cell 5 at time 7 = 7

then value of cell 5 at time 8 = 14

Proof:

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Given

1	instruction #3 is `addi dst=5 src=5 imm=7`
2	the PC at time 7 = 3
3	value of cell 5 at time 7 = 7

Proof Table

#	Claim	Reason
1	value of cell 5 at time (7 + 1) = (value of cell 5 at time 7) + 7	if instruction #3 is `addi dst=5 src=5 imm=7` and the PC at time 7 = 3, then value of cell 5 at time (7 + 1) = (value of cell 5 at time 7) + 7 (ADDI Instruction Property)
2	7 + 1 = 8	7 + 1 = 8 (Fixed Value Statement)
3	value of cell 5 at time (7 + 1) = value of cell 5 at time 8	if 7 + 1 = 8, then value of cell 5 at time (7 + 1) = value of cell 5 at time 8 (Substitution)
4	value of cell 5 at time 8 = (value of cell 5 at time 7) + 7	if value of cell 5 at time (7 + 1) = value of cell 5 at time 8 and value of cell 5 at time (7 + 1) = (value of cell 5 at time 7) + 7, then value of cell 5 at time 8 = (value of cell 5 at time 7) + 7 (Transitive Property of Equality Variation 2)
5	value of cell 5 at time 8 = 7 + 7	if value of cell 5 at time 8 = (value of cell 5 at time 7) + 7 and value of cell 5 at time 7 = 7, then value of cell 5 at time 8 = 7 + 7 (Term 1 Substitution)
6	7 + 7 = 14	7 + 7 = 14 (Fixed Value Statement)
7	value of cell 5 at time 8 = 14	if value of cell 5 at time 8 = 7 + 7 and 7 + 7 = 14, then value of cell 5 at time 8 = 14 (Transitive Property of Equality)

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