Proof: Addi Insn 19

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 19 = 7
value of cell 4 at time 19 = 2

then value of cell 4 at time 20 = 3

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 19 = 7
3	value of cell 4 at time 19 = 2

Proof Table

#	Claim	Reason
1	value of cell 4 at time (19 + 1) = (value of cell 4 at time 19) + 1	if instruction #7 is `addi dst=4 src=4 imm=1` and the PC at time 19 = 7, then value of cell 4 at time (19 + 1) = (value of cell 4 at time 19) + 1 (ADDI Instruction Property)
2	19 + 1 = 20	19 + 1 = 20 (Fixed Value Statement)
3	value of cell 4 at time (19 + 1) = value of cell 4 at time 20	if 19 + 1 = 20, then value of cell 4 at time (19 + 1) = value of cell 4 at time 20 (Substitution)
4	value of cell 4 at time 20 = (value of cell 4 at time 19) + 1	if value of cell 4 at time (19 + 1) = value of cell 4 at time 20 and value of cell 4 at time (19 + 1) = (value of cell 4 at time 19) + 1, then value of cell 4 at time 20 = (value of cell 4 at time 19) + 1 (Transitive Property of Equality Variation 2)
5	value of cell 4 at time 20 = 2 + 1	if value of cell 4 at time 20 = (value of cell 4 at time 19) + 1 and value of cell 4 at time 19 = 2, then value of cell 4 at time 20 = 2 + 1 (Term 1 Substitution)
6	2 + 1 = 3	2 + 1 = 3 (Fixed Value Statement)
7	value of cell 4 at time 20 = 3	if value of cell 4 at time 20 = 2 + 1 and 2 + 1 = 3, then value of cell 4 at time 20 = 3 (Transitive Property of Equality)

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