Proof: Byte 5 Stays the Same 8

Let's prove the following theorem:

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 8 = 8
value of cell 5 at time 8 = 4

then value of cell 5 at time 9 = 4

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #8 is `beq left=4 right=5 imm=1`
2	the PC at time 8 = 8
3	value of cell 5 at time 8 = 4

Proof Table

#	Claim	Reason
1	value of cell 5 at time (8 + 1) = value of cell 5 at time 8	if instruction #8 is `beq left=4 right=5 imm=1` and the PC at time 8 = 8, then value of cell 5 at time (8 + 1) = value of cell 5 at time 8 (BEQ Instruction Property 3)
2	8 + 1 = 9	8 + 1 = 9 (Fixed Value Statement)
3	value of cell 5 at time (8 + 1) = value of cell 5 at time 9	if 8 + 1 = 9, then value of cell 5 at time (8 + 1) = value of cell 5 at time 9 (Substitution)
4	value of cell 5 at time 9 = value of cell 5 at time 8	if value of cell 5 at time (8 + 1) = value of cell 5 at time 9 and value of cell 5 at time (8 + 1) = value of cell 5 at time 8, then value of cell 5 at time 9 = value of cell 5 at time 8 (Transitive Property of Equality Variation 2)
5	value of cell 5 at time 9 = 4	if value of cell 5 at time 9 = value of cell 5 at time 8 and value of cell 5 at time 8 = 4, then value of cell 5 at time 9 = 4 (Transitive Property of Equality)

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