Proof: Pc 18

Let's prove the following theorem:

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 18 = 6

then the PC at time 19 = 7

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #6 is `addi dst=2 src=3 imm=0`
2	the PC at time 18 = 6

Proof Table

#	Claim	Reason
1	the PC at time (18 + 1) = 6 + 1	if instruction #6 is `addi dst=2 src=3 imm=0` and the PC at time 18 = 6, then the PC at time (18 + 1) = 6 + 1 (Program Counter on ADDI)
2	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
3	6 + 1 = 7	6 + 1 = 7 (Fixed Value Statement)
4	the PC at time (18 + 1) = the PC at time 19	if 18 + 1 = 19, then the PC at time (18 + 1) = the PC at time 19 (Substitution)
5	the PC at time 19 = 7	if the PC at time (18 + 1) = 6 + 1 and the PC at time (18 + 1) = the PC at time 19 and 6 + 1 = 7, then the PC at time 19 = 7 (Transitive Property Application 2)

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