Proof: Pc 17

Let's prove the following theorem:

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 17 = 5

then the PC at time 18 = 6

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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

Given

1	instruction #5 is `addi dst=1 src=2 imm=0`
2	the PC at time 17 = 5

Proof Table

#	Claim	Reason
1	the PC at time (17 + 1) = 5 + 1	if instruction #5 is `addi dst=1 src=2 imm=0` and the PC at time 17 = 5, then the PC at time (17 + 1) = 5 + 1 (Program Counter on ADDI)
2	17 + 1 = 18	17 + 1 = 18 (Fixed Value Statement)
3	5 + 1 = 6	5 + 1 = 6 (Fixed Value Statement)
4	the PC at time (17 + 1) = the PC at time 18	if 17 + 1 = 18, then the PC at time (17 + 1) = the PC at time 18 (Substitution)
5	the PC at time 18 = 6	if the PC at time (17 + 1) = 5 + 1 and the PC at time (17 + 1) = the PC at time 18 and 5 + 1 = 6, then the PC at time 18 = 6 (Transitive Property Application 2)

Comments

Please log in to add comments