Transitive Property of Equality Variation 2
Transitive Property Application 2
Pc 19

Proof: Pc 19

Let's prove the following theorem:

if the following are true:
  • instruction #7 is addi dst=4 src=4 imm=1
  • the PC at time 19 = 7

then the PC at time 20 = 8

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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Given
1 instruction #7 is addi dst=4 src=4 imm=1
2 the PC at time 19 = 7
Proof Table
# Claim Reason
1 the PC at time (19 + 1) = 7 + 1 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 19 = 7, then the PC at time (19 + 1) = 7 + 1
2 19 + 1 = 20 19 + 1 = 20
3 7 + 1 = 8 7 + 1 = 8
4 the PC at time (19 + 1) = the PC at time 20 if 19 + 1 = 20, then the PC at time (19 + 1) = the PC at time 20
5 the PC at time 20 = 8 if the PC at time (19 + 1) = 7 + 1 and the PC at time (19 + 1) = the PC at time 20 and 7 + 1 = 8, then the PC at time 20 = 8
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