Proof: Byte 3 Stays the Same 5

Let's prove the following theorem:

if the following are true:
  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 5 = 5
  • value of cell 3 at time 5 = 3

then value of cell 3 at time 6 = 3

Proof:

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

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