Proof: Jump Help 13

Let's prove the following theorem:

if the following are true:
  • instruction #6 is jump imm=0
  • the PC at time 13 = 6

then the PC at time 14 = 0

Proof:

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Given
1 instruction #6 is jump imm=0
2 the PC at time 13 = 6
Proof Table
# Claim Reason
1 the PC at time (13 + 1) = 0 if instruction #6 is jump imm=0 and the PC at time 13 = 6, then the PC at time (13 + 1) = 0
2 13 + 1 = 14 13 + 1 = 14
3 the PC at time (13 + 1) = the PC at time 14 if 13 + 1 = 14, then the PC at time (13 + 1) = the PC at time 14
4 the PC at time 14 = 0 if the PC at time (13 + 1) = the PC at time 14 and the PC at time (13 + 1) = 0, then the PC at time 14 = 0

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