Proof: Pc 22

Let's prove the following theorem:

if the following are true:

instruction #22 is addi dst=1 src=1 imm=3
the PC at time 22 = 22

then the PC at time 23 = 23

Proof:

View as a tree | View dependent proofs | Try proving it

Given

1	instruction #22 is `addi dst=1 src=1 imm=3`
2	the PC at time 22 = 22

Proof Table

#	Claim	Reason
1	the PC at time (22 + 1) = 22 + 1	if instruction #22 is `addi dst=1 src=1 imm=3` and the PC at time 22 = 22, then the PC at time (22 + 1) = 22 + 1 (Program Counter on ADDI)
2	22 + 1 = 23	22 + 1 = 23 (Fixed Value Statement)
3	the PC at time (22 + 1) = the PC at time 23	if 22 + 1 = 23, then the PC at time (22 + 1) = the PC at time 23 (Substitution)
4	the PC at time 23 = 23	if the PC at time (22 + 1) = 22 + 1 and the PC at time (22 + 1) = the PC at time 23 and 22 + 1 = 23, then the PC at time 23 = 23 (Transitive Property Application 2)

Comments

Please log in to add comments