Proof: Beq Branch

Let's prove the following theorem:

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 13 = 5
value of cell 3 at time 13 = 3
value of cell 4 at time 13 = 3

then the PC at time 14 = 7

Proof:

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Given

1	instruction #5 is `beq left=3 right=4 imm=1`
2	the PC at time 13 = 5
3	value of cell 3 at time 13 = 3
4	value of cell 4 at time 13 = 3

Proof Table

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

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