Proof: Pc 13

Let's prove the following theorem:

if the following are true:

instruction #19 is store src=3 addr=1 imm=0
the PC at time 13 = 19

then the PC at time 14 = 20

Proof:

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Given

1	instruction #19 is `store src=3 addr=1 imm=0`
2	the PC at time 13 = 19

Proof Table

#	Claim	Reason
1	the PC at time (13 + 1) = 19 + 1	if instruction #19 is `store src=3 addr=1 imm=0` and the PC at time 13 = 19, then the PC at time (13 + 1) = 19 + 1 (STORE Instruction Property 3)
2	13 + 1 = 14	13 + 1 = 14 (Fixed Value Statement)
3	19 + 1 = 20	19 + 1 = 20 (Fixed Value Statement)
4	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)
5	the PC at time 14 = 20	if the PC at time (13 + 1) = 19 + 1 and the PC at time (13 + 1) = the PC at time 14 and 19 + 1 = 20, then the PC at time 14 = 20 (Transitive Property Application 2)

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