Proof: Load 21

Let's prove the following theorem:

if the following are true:
  • instruction #21 is load dst=3 addr=1 imm=0
  • the PC at time 21 = 21
  • value of cell 1 at time 21 = 123
  • value of cell 123 at time 21 = 5

then value of cell 3 at time 22 = 5

Proof:

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Given
1 instruction #21 is load dst=3 addr=1 imm=0
2 the PC at time 21 = 21
3 value of cell 1 at time 21 = 123
4 value of cell 123 at time 21 = 5
Proof Table
# Claim Reason
1 value of cell 3 at time (21 + 1) = value of cell ((value of cell 1 at time 21) + 0) at time 21 if instruction #21 is load dst=3 addr=1 imm=0 and the PC at time 21 = 21, then value of cell 3 at time (21 + 1) = value of cell ((value of cell 1 at time 21) + 0) at time 21
2 (value of cell 1 at time 21) + 0 = 123 + 0 if value of cell 1 at time 21 = 123, then (value of cell 1 at time 21) + 0 = 123 + 0
3 123 + 0 = 123 123 + 0 = 123
4 (value of cell 1 at time 21) + 0 = 123 if (value of cell 1 at time 21) + 0 = 123 + 0 and 123 + 0 = 123, then (value of cell 1 at time 21) + 0 = 123
5 value of cell ((value of cell 1 at time 21) + 0) at time 21 = value of cell 123 at time 21 if (value of cell 1 at time 21) + 0 = 123, then value of cell ((value of cell 1 at time 21) + 0) at time 21 = value of cell 123 at time 21
6 value of cell ((value of cell 1 at time 21) + 0) at time 21 = 5 if value of cell ((value of cell 1 at time 21) + 0) at time 21 = value of cell 123 at time 21 and value of cell 123 at time 21 = 5, then value of cell ((value of cell 1 at time 21) + 0) at time 21 = 5
7 value of cell 3 at time (21 + 1) = 5 if value of cell 3 at time (21 + 1) = value of cell ((value of cell 1 at time 21) + 0) at time 21 and value of cell ((value of cell 1 at time 21) + 0) at time 21 = 5, then value of cell 3 at time (21 + 1) = 5
8 21 + 1 = 22 21 + 1 = 22
9 value of cell 3 at time (21 + 1) = value of cell 3 at time 22 if 21 + 1 = 22, then value of cell 3 at time (21 + 1) = value of cell 3 at time 22
10 value of cell 3 at time 22 = 5 if value of cell 3 at time (21 + 1) = value of cell 3 at time 22 and value of cell 3 at time (21 + 1) = 5, then value of cell 3 at time 22 = 5

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