Transitive Property of Equality Variation 2

Transitive Property Application 2

Pc 7

Proof: Pc 7

Let's prove the following theorem:

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 7 = 7

then the PC at time 8 = 8

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #7 is `addi dst=4 src=4 imm=1`
2	the PC at time 7 = 7

Proof Table

#	Claim	Reason
1	the PC at time (7 + 1) = 7 + 1	if instruction #7 is `addi dst=4 src=4 imm=1` and the PC at time 7 = 7, then the PC at time (7 + 1) = 7 + 1 (Program Counter on ADDI)
2	7 + 1 = 8	7 + 1 = 8 (Fixed Value Statement)
3	the PC at time (7 + 1) = the PC at time 8	if 7 + 1 = 8, then the PC at time (7 + 1) = the PC at time 8 (Substitution)
4	the PC at time 8 = 8	if the PC at time (7 + 1) = 7 + 1 and the PC at time (7 + 1) = the PC at time 8 and 7 + 1 = 8, then the PC at time 8 = 8 (Transitive Property Application 2)

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