Proof: Addi Insn 13

Let's prove the following theorem:

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 13 = 7
value of cell 4 at time 13 = 1

then value of cell 4 at time 14 = 2

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #7 is `addi dst=4 src=4 imm=1`
2	the PC at time 13 = 7
3	value of cell 4 at time 13 = 1

Proof Table

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

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