Proof: Byte 4 Stays the Same 1

Let's prove the following theorem:

if the following are true:

instruction #1 is addi dst=8 src=4 imm=0
the PC at time 1 = 1
value of cell 4 at time 1 = 11

then value of cell 4 at time 2 = 11

Proof:

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

Given

1	instruction #1 is `addi dst=8 src=4 imm=0`
2	the PC at time 1 = 1
3	value of cell 4 at time 1 = 11

Proof Table

#	Claim	Reason
1	not (4 = 8)	not (4 = 8) (Fixed Value Statement)
2	value of cell 4 at time (1 + 1) = value of cell 4 at time 1	if instruction #1 is `addi dst=8 src=4 imm=0` and the PC at time 1 = 1 and not (4 = 8), then value of cell 4 at time (1 + 1) = value of cell 4 at time 1 (ADDI Instruction Property 2)
3	1 + 1 = 2	1 + 1 = 2 (Fixed Value Statement)
4	value of cell 4 at time (1 + 1) = value of cell 4 at time 2	if 1 + 1 = 2, then value of cell 4 at time (1 + 1) = value of cell 4 at time 2 (Substitution)
5	value of cell 4 at time 2 = value of cell 4 at time 1	if value of cell 4 at time (1 + 1) = value of cell 4 at time 2 and value of cell 4 at time (1 + 1) = value of cell 4 at time 1, then value of cell 4 at time 2 = value of cell 4 at time 1 (Transitive Property of Equality Variation 2)
6	value of cell 4 at time 2 = 11	if value of cell 4 at time 2 = value of cell 4 at time 1 and value of cell 4 at time 1 = 11, then value of cell 4 at time 2 = 11 (Transitive Property of Equality)

Comments

Please log in to add comments