Proof: Byte 4 Stays the Same 16

Let's prove the following theorem:

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 16 = 4
value of cell 4 at time 16 = 2

then value of cell 4 at time 17 = 2

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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

Given

1	instruction #4 is `add dst=3 src1=1 src2=2`
2	the PC at time 16 = 4
3	value of cell 4 at time 16 = 2

Proof Table

#	Claim	Reason
1	not (4 = 3)	not (4 = 3) (Fixed Value Statement)
2	value of cell 4 at time (16 + 1) = value of cell 4 at time 16	if instruction #4 is `add dst=3 src1=1 src2=2` and the PC at time 16 = 4 and not (4 = 3), then value of cell 4 at time (16 + 1) = value of cell 4 at time 16 (ADD Instruction Property 2)
3	16 + 1 = 17	16 + 1 = 17 (Fixed Value Statement)
4	value of cell 4 at time (16 + 1) = value of cell 4 at time 17	if 16 + 1 = 17, then value of cell 4 at time (16 + 1) = value of cell 4 at time 17 (Substitution)
5	value of cell 4 at time 17 = value of cell 4 at time 16	if value of cell 4 at time (16 + 1) = value of cell 4 at time 17 and value of cell 4 at time (16 + 1) = value of cell 4 at time 16, then value of cell 4 at time 17 = value of cell 4 at time 16 (Transitive Property of Equality Variation 2)
6	value of cell 4 at time 17 = 2	if value of cell 4 at time 17 = value of cell 4 at time 16 and value of cell 4 at time 16 = 2, then value of cell 4 at time 17 = 2 (Transitive Property of Equality)

Comments

Please log in to add comments