Proof: Addi Insn 3

Let's prove the following theorem:

if the following are true:

instruction #3 is addi dst=5 src=5 imm=7
the PC at time 3 = 3
value of cell 5 at time 3 = 0

then value of cell 5 at time 4 = 7

Proof:

View as a tree | View dependent proofs | Try proving it

Given

1	instruction #3 is `addi dst=5 src=5 imm=7`
2	the PC at time 3 = 3
3	value of cell 5 at time 3 = 0

Proof Table

#	Claim	Reason
1	value of cell 5 at time (3 + 1) = (value of cell 5 at time 3) + 7	if instruction #3 is `addi dst=5 src=5 imm=7` and the PC at time 3 = 3, then value of cell 5 at time (3 + 1) = (value of cell 5 at time 3) + 7 (ADDI Instruction Property)
2	3 + 1 = 4	3 + 1 = 4 (Fixed Value Statement)
3	value of cell 5 at time (3 + 1) = value of cell 5 at time 4	if 3 + 1 = 4, then value of cell 5 at time (3 + 1) = value of cell 5 at time 4 (Substitution)
4	value of cell 5 at time 4 = (value of cell 5 at time 3) + 7	if value of cell 5 at time (3 + 1) = value of cell 5 at time 4 and value of cell 5 at time (3 + 1) = (value of cell 5 at time 3) + 7, then value of cell 5 at time 4 = (value of cell 5 at time 3) + 7 (Transitive Property of Equality Variation 2)
5	value of cell 5 at time 4 = 0 + 7	if value of cell 5 at time 4 = (value of cell 5 at time 3) + 7 and value of cell 5 at time 3 = 0, then value of cell 5 at time 4 = 0 + 7 (Term 1 Substitution)
6	0 + 7 = 7	0 + 7 = 7 (Additive Identity Variation)
7	value of cell 5 at time 4 = 7	if value of cell 5 at time 4 = 0 + 7 and 0 + 7 = 7, then value of cell 5 at time 4 = 7 (Transitive Property of Equality)

Comments

Please log in to add comments