Proof: Load 15

Let's prove the following theorem:

if the following are true:
  • instruction #2 is load dst=3 addr=1 imm=1
  • the PC at time 15 = 2
  • value of cell 1 at time 15 = 124
  • value of cell 125 at time 15 = 2

then value of cell 3 at time 16 = 2

Proof:

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Given
1 instruction #2 is load dst=3 addr=1 imm=1
2 the PC at time 15 = 2
3 value of cell 1 at time 15 = 124
4 value of cell 125 at time 15 = 2
Proof Table
# Claim Reason
1 value of cell 3 at time (15 + 1) = value of cell ((value of cell 1 at time 15) + 1) at time 15 if instruction #2 is load dst=3 addr=1 imm=1 and the PC at time 15 = 2, then value of cell 3 at time (15 + 1) = value of cell ((value of cell 1 at time 15) + 1) at time 15
2 (value of cell 1 at time 15) + 1 = 124 + 1 if value of cell 1 at time 15 = 124, then (value of cell 1 at time 15) + 1 = 124 + 1
3 124 + 1 = 125 124 + 1 = 125
4 (value of cell 1 at time 15) + 1 = 125 if (value of cell 1 at time 15) + 1 = 124 + 1 and 124 + 1 = 125, then (value of cell 1 at time 15) + 1 = 125
5 value of cell ((value of cell 1 at time 15) + 1) at time 15 = value of cell 125 at time 15 if (value of cell 1 at time 15) + 1 = 125, then value of cell ((value of cell 1 at time 15) + 1) at time 15 = value of cell 125 at time 15
6 value of cell ((value of cell 1 at time 15) + 1) at time 15 = 2 if value of cell ((value of cell 1 at time 15) + 1) at time 15 = value of cell 125 at time 15 and value of cell 125 at time 15 = 2, then value of cell ((value of cell 1 at time 15) + 1) at time 15 = 2
7 value of cell 3 at time (15 + 1) = 2 if value of cell 3 at time (15 + 1) = value of cell ((value of cell 1 at time 15) + 1) at time 15 and value of cell ((value of cell 1 at time 15) + 1) at time 15 = 2, then value of cell 3 at time (15 + 1) = 2
8 15 + 1 = 16 15 + 1 = 16
9 value of cell 3 at time (15 + 1) = value of cell 3 at time 16 if 15 + 1 = 16, then value of cell 3 at time (15 + 1) = value of cell 3 at time 16
10 value of cell 3 at time 16 = 2 if value of cell 3 at time (15 + 1) = value of cell 3 at time 16 and value of cell 3 at time (15 + 1) = 2, then value of cell 3 at time 16 = 2

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