Proof: Store 13

Let's prove the following theorem:

if the following are true:

instruction #19 is store src=3 addr=1 imm=0
the PC at time 13 = 19
value of cell 1 at time 13 = 124
value of cell 3 at time 13 = 3

then value of cell 124 at time 14 = 3

Proof:

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Given

1	instruction #19 is `store src=3 addr=1 imm=0`
2	the PC at time 13 = 19
3	value of cell 1 at time 13 = 124
4	value of cell 3 at time 13 = 3

Proof Table

#	Claim	Reason
1	value of cell ((value of cell 1 at time 13) + 0) at time (13 + 1) = value of cell 3 at time 13	if instruction #19 is `store src=3 addr=1 imm=0` and the PC at time 13 = 19, then value of cell ((value of cell 1 at time 13) + 0) at time (13 + 1) = value of cell 3 at time 13 (Store Instruction Property)
2	(value of cell 1 at time 13) + 0 = 124 + 0	if value of cell 1 at time 13 = 124, then (value of cell 1 at time 13) + 0 = 124 + 0 (Additive Property of Equality)
3	124 + 0 = 124	124 + 0 = 124 (Additive Identity)
4	(value of cell 1 at time 13) + 0 = 124	if (value of cell 1 at time 13) + 0 = 124 + 0 and 124 + 0 = 124, then (value of cell 1 at time 13) + 0 = 124 (Transitive Property of Equality)
5	value of cell ((value of cell 1 at time 13) + 0) at time (13 + 1) = value of cell 124 at time (13 + 1)	if (value of cell 1 at time 13) + 0 = 124, then value of cell ((value of cell 1 at time 13) + 0) at time (13 + 1) = value of cell 124 at time (13 + 1) (Substitution)
6	13 + 1 = 14	13 + 1 = 14 (Fixed Value Statement)
7	value of cell 124 at time (13 + 1) = value of cell 124 at time 14	if 13 + 1 = 14, then value of cell 124 at time (13 + 1) = value of cell 124 at time 14 (Substitution)
8	value of cell 124 at time 14 = value of cell 3 at time 13	if value of cell ((value of cell 1 at time 13) + 0) at time (13 + 1) = value of cell 124 at time (13 + 1) and value of cell 124 at time (13 + 1) = value of cell 124 at time 14 and value of cell ((value of cell 1 at time 13) + 0) at time (13 + 1) = value of cell 3 at time 13, then value of cell 124 at time 14 = value of cell 3 at time 13 (Transitive With Four)
9	value of cell 124 at time 14 = 3	if value of cell 124 at time 14 = value of cell 3 at time 13 and value of cell 3 at time 13 = 3, then value of cell 124 at time 14 = 3 (Transitive Property of Equality)

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