Proof: Addi Insn 11

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 11 = 3
value of cell 5 at time 11 = 14

then value of cell 5 at time 12 = 21

Proof:

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Given

1	instruction #3 is `addi dst=5 src=5 imm=7`
2	the PC at time 11 = 3
3	value of cell 5 at time 11 = 14

Proof Table

#	Claim	Reason
1	value of cell 5 at time (11 + 1) = (value of cell 5 at time 11) + 7	if instruction #3 is `addi dst=5 src=5 imm=7` and the PC at time 11 = 3, then value of cell 5 at time (11 + 1) = (value of cell 5 at time 11) + 7 (ADDI Instruction Property)
2	11 + 1 = 12	11 + 1 = 12 (Fixed Value Statement)
3	value of cell 5 at time (11 + 1) = value of cell 5 at time 12	if 11 + 1 = 12, then value of cell 5 at time (11 + 1) = value of cell 5 at time 12 (Substitution)
4	value of cell 5 at time 12 = (value of cell 5 at time 11) + 7	if value of cell 5 at time (11 + 1) = value of cell 5 at time 12 and value of cell 5 at time (11 + 1) = (value of cell 5 at time 11) + 7, then value of cell 5 at time 12 = (value of cell 5 at time 11) + 7 (Transitive Property of Equality Variation 2)
5	value of cell 5 at time 12 = 14 + 7	if value of cell 5 at time 12 = (value of cell 5 at time 11) + 7 and value of cell 5 at time 11 = 14, then value of cell 5 at time 12 = 14 + 7 (Term 1 Substitution)
6	14 + 7 = 21	14 + 7 = 21 (Fixed Value Statement)
7	value of cell 5 at time 12 = 21	if value of cell 5 at time 12 = 14 + 7 and 14 + 7 = 21, then value of cell 5 at time 12 = 21 (Transitive Property of Equality)

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