Proof: Addi Insn 10

Let's prove the following theorem:

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 10 = 3
value of cell 6 at time 10 = 13

then value of cell 6 at time 11 = 14

Proof:

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Given

1	instruction #3 is `addi dst=6 src=6 imm=1`
2	the PC at time 10 = 3
3	value of cell 6 at time 10 = 13

Proof Table

#	Claim	Reason
1	value of cell 6 at time (10 + 1) = (value of cell 6 at time 10) + 1	if instruction #3 is `addi dst=6 src=6 imm=1` and the PC at time 10 = 3, then value of cell 6 at time (10 + 1) = (value of cell 6 at time 10) + 1 (ADDI Instruction Property)
2	10 + 1 = 11	10 + 1 = 11 (Fixed Value Statement)
3	value of cell 6 at time (10 + 1) = value of cell 6 at time 11	if 10 + 1 = 11, then value of cell 6 at time (10 + 1) = value of cell 6 at time 11 (Substitution)
4	value of cell 6 at time 11 = (value of cell 6 at time 10) + 1	if value of cell 6 at time (10 + 1) = value of cell 6 at time 11 and value of cell 6 at time (10 + 1) = (value of cell 6 at time 10) + 1, then value of cell 6 at time 11 = (value of cell 6 at time 10) + 1 (Transitive Property of Equality Variation 2)
5	value of cell 6 at time 11 = 13 + 1	if value of cell 6 at time 11 = (value of cell 6 at time 10) + 1 and value of cell 6 at time 10 = 13, then value of cell 6 at time 11 = 13 + 1 (Term 1 Substitution)
6	13 + 1 = 14	13 + 1 = 14 (Fixed Value Statement)
7	value of cell 6 at time 11 = 14	if value of cell 6 at time 11 = 13 + 1 and 13 + 1 = 14, then value of cell 6 at time 11 = 14 (Transitive Property of Equality)

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