Proof: Store 19

Let's prove the following theorem:

if the following are true:

instruction #6 is store src=3 addr=1 imm=0
the PC at time 19 = 6
value of cell 1 at time 19 = 123
value of cell 3 at time 19 = 5

then value of cell 123 at time 20 = 5

Proof:

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Given

1	instruction #6 is `store src=3 addr=1 imm=0`
2	the PC at time 19 = 6
3	value of cell 1 at time 19 = 123
4	value of cell 3 at time 19 = 5

Proof Table

#	Claim	Reason
1	value of cell ((value of cell 1 at time 19) + 0) at time (19 + 1) = value of cell 3 at time 19	if instruction #6 is `store src=3 addr=1 imm=0` and the PC at time 19 = 6, then value of cell ((value of cell 1 at time 19) + 0) at time (19 + 1) = value of cell 3 at time 19 (Store Instruction Property)
2	(value of cell 1 at time 19) + 0 = 123 + 0	if value of cell 1 at time 19 = 123, then (value of cell 1 at time 19) + 0 = 123 + 0 (Additive Property of Equality)
3	123 + 0 = 123	123 + 0 = 123 (Additive Identity)
4	(value of cell 1 at time 19) + 0 = 123	if (value of cell 1 at time 19) + 0 = 123 + 0 and 123 + 0 = 123, then (value of cell 1 at time 19) + 0 = 123 (Transitive Property of Equality)
5	value of cell ((value of cell 1 at time 19) + 0) at time (19 + 1) = value of cell 123 at time (19 + 1)	if (value of cell 1 at time 19) + 0 = 123, then value of cell ((value of cell 1 at time 19) + 0) at time (19 + 1) = value of cell 123 at time (19 + 1) (Substitution)
6	19 + 1 = 20	19 + 1 = 20 (Fixed Value Statement)
7	value of cell 123 at time (19 + 1) = value of cell 123 at time 20	if 19 + 1 = 20, then value of cell 123 at time (19 + 1) = value of cell 123 at time 20 (Substitution)
8	value of cell 123 at time 20 = value of cell 3 at time 19	if value of cell ((value of cell 1 at time 19) + 0) at time (19 + 1) = value of cell 123 at time (19 + 1) and value of cell 123 at time (19 + 1) = value of cell 123 at time 20 and value of cell ((value of cell 1 at time 19) + 0) at time (19 + 1) = value of cell 3 at time 19, then value of cell 123 at time 20 = value of cell 3 at time 19 (Transitive With Four)
9	value of cell 123 at time 20 = 5	if value of cell 123 at time 20 = value of cell 3 at time 19 and value of cell 3 at time 19 = 5, then value of cell 123 at time 20 = 5 (Transitive Property of Equality)

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