Proof: Addi Insn 17

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 17 = 3
value of cell 6 at time 17 = 14

then value of cell 6 at time 18 = 15

Proof:

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Given

1	instruction #3 is `addi dst=6 src=6 imm=1`
2	the PC at time 17 = 3
3	value of cell 6 at time 17 = 14

Proof Table

#	Claim	Reason
1	value of cell 6 at time (17 + 1) = (value of cell 6 at time 17) + 1	if instruction #3 is `addi dst=6 src=6 imm=1` and the PC at time 17 = 3, then value of cell 6 at time (17 + 1) = (value of cell 6 at time 17) + 1 (ADDI Instruction Property)
2	17 + 1 = 18	17 + 1 = 18 (Fixed Value Statement)
3	value of cell 6 at time (17 + 1) = value of cell 6 at time 18	if 17 + 1 = 18, then value of cell 6 at time (17 + 1) = value of cell 6 at time 18 (Substitution)
4	value of cell 6 at time 18 = (value of cell 6 at time 17) + 1	if value of cell 6 at time (17 + 1) = value of cell 6 at time 18 and value of cell 6 at time (17 + 1) = (value of cell 6 at time 17) + 1, then value of cell 6 at time 18 = (value of cell 6 at time 17) + 1 (Transitive Property of Equality Variation 2)
5	value of cell 6 at time 18 = 14 + 1	if value of cell 6 at time 18 = (value of cell 6 at time 17) + 1 and value of cell 6 at time 17 = 14, then value of cell 6 at time 18 = 14 + 1 (Term 1 Substitution)
6	14 + 1 = 15	14 + 1 = 15 (Fixed Value Statement)
7	value of cell 6 at time 18 = 15	if value of cell 6 at time 18 = 14 + 1 and 14 + 1 = 15, then value of cell 6 at time 18 = 15 (Transitive Property of Equality)

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