Proof: Byte 3 Stays the Same 6

Let's prove the following theorem:

if the following are true:
  • instruction #6 is jump imm=3
  • the PC at time 6 = 6
  • value of cell 3 at time 6 = 3

then value of cell 3 at time 7 = 3

Proof:

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Given
1 instruction #6 is jump imm=3
2 the PC at time 6 = 6
3 value of cell 3 at time 6 = 3
Proof Table
# Claim Reason
1 value of cell 3 at time (6 + 1) = value of cell 3 at time 6 if instruction #6 is jump imm=3 and the PC at time 6 = 6, then value of cell 3 at time (6 + 1) = value of cell 3 at time 6
2 6 + 1 = 7 6 + 1 = 7
3 value of cell 3 at time (6 + 1) = value of cell 3 at time 7 if 6 + 1 = 7, then value of cell 3 at time (6 + 1) = value of cell 3 at time 7
4 value of cell 3 at time 7 = value of cell 3 at time 6 if value of cell 3 at time (6 + 1) = value of cell 3 at time 7 and value of cell 3 at time (6 + 1) = value of cell 3 at time 6, then value of cell 3 at time 7 = value of cell 3 at time 6
5 value of cell 3 at time 7 = 3 if value of cell 3 at time 7 = value of cell 3 at time 6 and value of cell 3 at time 6 = 3, then value of cell 3 at time 7 = 3

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