Proof: Addi Zero Insn 3

Let's prove the following theorem:

if the following are true:

instruction #3 is addi dst=5 src=0 imm=4
the PC at time 3 = 3

then value of cell 5 at time 4 = 4

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #3 is `addi dst=5 src=0 imm=4`
2	the PC at time 3 = 3

Proof Table

#	Claim	Reason
1	value of cell 5 at time (3 + 1) = 4	if instruction #3 is `addi dst=5 src=0 imm=4` and the PC at time 3 = 3, then value of cell 5 at time (3 + 1) = 4 (Addi to Zero)
2	3 + 1 = 4	3 + 1 = 4 (Fixed Value Statement)
3	value of cell 5 at time (3 + 1) = value of cell 5 at time 4	if 3 + 1 = 4, then value of cell 5 at time (3 + 1) = value of cell 5 at time 4 (Substitution)
4	value of cell 5 at time 4 = 4	if value of cell 5 at time (3 + 1) = value of cell 5 at time 4 and value of cell 5 at time (3 + 1) = 4, then value of cell 5 at time 4 = 4 (Transitive Property of Equality Variation 2)

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