Proof: Jal 14

Let's prove the following theorem:

if the following are true:

instruction #20 is a JAL instruction with jump to: 2
the PC at time 14 = 20

then the PC at time 15 = 2

Proof:

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Given

1	instruction #20 is a JAL instruction with jump to: 2
2	the PC at time 14 = 20

Proof Table

#	Claim	Reason
1	the PC at time (14 + 1) = 2	if instruction #20 is a JAL instruction with jump to: 2 and the PC at time 14 = 20, then the PC at time (14 + 1) = 2 (JAL Instruction Property)
2	14 + 1 = 15	14 + 1 = 15 (Fixed Value Statement)
3	the PC at time (14 + 1) = the PC at time 15	if 14 + 1 = 15, then the PC at time (14 + 1) = the PC at time 15 (Substitution)
4	the PC at time 15 = 2	if the PC at time (14 + 1) = the PC at time 15 and the PC at time (14 + 1) = 2, then the PC at time 15 = 2 (Transitive Property of Equality Variation 2)

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