Proof: Jump Help 6

Let's prove the following theorem:

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

then the PC at time 7 = 3

Proof:

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

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