Proof: STORE Instruction Example 3

Let's prove the following theorem:

if the following are true:

instruction #0 is store src=5 addr=1 imm=1
the PC at time 0 = 0
value of cell 1 at time 0 = 3

then value of cell 2 at time 1 = value of cell 2 at time 0

The following example shows that when a STORE instruction with src = 5, addr = 1, and imm = 1 is executed, memory cell #4 is updated to a new value (9), but other cells, such as cell #2, remain unchanged.

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #0 is `store src=5 addr=1 imm=1`
2	the PC at time 0 = 0
3	value of cell 1 at time 0 = 3

Proof Table

#	Claim	Reason
1	(value of cell 1 at time 0) + 1 = 3 + 1	if value of cell 1 at time 0 = 3, then (value of cell 1 at time 0) + 1 = 3 + 1 (Substitution)
2	3 + 1 = 4	3 + 1 = 4 (Fixed Value Statement)
3	(value of cell 1 at time 0) + 1 = 4	if (value of cell 1 at time 0) + 1 = 3 + 1 and 3 + 1 = 4, then (value of cell 1 at time 0) + 1 = 4 (Transitive Property of Equality)
4	2 = (value of cell 1 at time 0) + 1 = 2 = 4	if (value of cell 1 at time 0) + 1 = 4, then 2 = (value of cell 1 at time 0) + 1 = 2 = 4 (Substitution)
5	not (2 = (value of cell 1 at time 0) + 1) = not (2 = 4)	if 2 = (value of cell 1 at time 0) + 1 = 2 = 4, then not (2 = (value of cell 1 at time 0) + 1) = not (2 = 4) (Substitution)
6	not (2 = 4)	not (2 = 4) (Fixed Value Statement)
7	not (2 = (value of cell 1 at time 0) + 1)	if not (2 = 4) and not (2 = (value of cell 1 at time 0) + 1) = not (2 = 4), then not (2 = (value of cell 1 at time 0) + 1) (Truth Propagation Property 2)
8	value of cell 2 at time (0 + 1) = value of cell 2 at time 0	if instruction #0 is `store src=5 addr=1 imm=1` and the PC at time 0 = 0 and not (2 = (value of cell 1 at time 0) + 1), then value of cell 2 at time (0 + 1) = value of cell 2 at time 0 (Store Instruction Property 2)
9	0 + 1 = 1	0 + 1 = 1 (Additive Identity Variation)
10	value of cell 2 at time (0 + 1) = value of cell 2 at time 1	if 0 + 1 = 1, then value of cell 2 at time (0 + 1) = value of cell 2 at time 1 (Substitution)
11	value of cell 2 at time 1 = value of cell 2 at time 0	if value of cell 2 at time (0 + 1) = value of cell 2 at time 1 and value of cell 2 at time (0 + 1) = value of cell 2 at time 0, then value of cell 2 at time 1 = value of cell 2 at time 0 (Transitive Property of Equality Variation 2)

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