Proof: Jump Help 15

Let's prove the following theorem:

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 15 = 9

then the PC at time 16 = 4

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #9 is `jump imm=(-6)`
2	the PC at time 15 = 9

Proof Table

#	Claim	Reason
1	the PC at time (15 + 1) = (9 + 1) + (-6)	if instruction #9 is `jump imm=(-6)` and the PC at time 15 = 9, then the PC at time (15 + 1) = (9 + 1) + (-6) (JUMP Instruction Property)
2	15 + 1 = 16	15 + 1 = 16 (Fixed Value Statement)
3	the PC at time (15 + 1) = the PC at time 16	if 15 + 1 = 16, then the PC at time (15 + 1) = the PC at time 16 (Substitution)
4	the PC at time 16 = (9 + 1) + (-6)	if the PC at time (15 + 1) = the PC at time 16 and the PC at time (15 + 1) = (9 + 1) + (-6), then the PC at time 16 = (9 + 1) + (-6) (Transitive Property of Equality Variation 2)
5	(9 + 1) + (-6) = 4	(9 + 1) + (-6) = 4 (Fixed Value Statement)
6	the PC at time 16 = 4	if the PC at time 16 = (9 + 1) + (-6) and (9 + 1) + (-6) = 4, then the PC at time 16 = 4 (Transitive Property of Equality)

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