Proof: Addi Insn 7

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 7 = 7
value of cell 4 at time 7 = 0

then value of cell 4 at time 8 = 1

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 7 = 7
3	value of cell 4 at time 7 = 0

Proof Table

#	Claim	Reason
1	value of cell 4 at time (7 + 1) = (value of cell 4 at time 7) + 1	if instruction #7 is `addi dst=4 src=4 imm=1` and the PC at time 7 = 7, then value of cell 4 at time (7 + 1) = (value of cell 4 at time 7) + 1 (ADDI Instruction Property)
2	7 + 1 = 8	7 + 1 = 8 (Fixed Value Statement)
3	value of cell 4 at time (7 + 1) = value of cell 4 at time 8	if 7 + 1 = 8, then value of cell 4 at time (7 + 1) = value of cell 4 at time 8 (Substitution)
4	value of cell 4 at time 8 = (value of cell 4 at time 7) + 1	if value of cell 4 at time (7 + 1) = value of cell 4 at time 8 and value of cell 4 at time (7 + 1) = (value of cell 4 at time 7) + 1, then value of cell 4 at time 8 = (value of cell 4 at time 7) + 1 (Transitive Property of Equality Variation 2)
5	value of cell 4 at time 8 = 0 + 1	if value of cell 4 at time 8 = (value of cell 4 at time 7) + 1 and value of cell 4 at time 7 = 0, then value of cell 4 at time 8 = 0 + 1 (Term 1 Substitution)
6	0 + 1 = 1	0 + 1 = 1 (Additive Identity Variation)
7	value of cell 4 at time 8 = 1	if value of cell 4 at time 8 = 0 + 1 and 0 + 1 = 1, then value of cell 4 at time 8 = 1 (Transitive Property of Equality)

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