Commutative Property Variation 1
Substitution 2
Substitution 6
Zero Plus a
Addi to Zero
Transitive Property of Equality Variation 2
Addi Zero Insn 0
Transitive Property Application 2
Pc 0
Addi Zero Insn 1
Pc 1
Byte 1 Stays the Same 1
Addi Zero Insn 2
Pc 2
Byte 1 Stays the Same 2
Byte 2 Stays the Same 2
Addi Zero Insn 3
Pc 3
Byte 1 Stays the Same 3
Byte 2 Stays the Same 3
Byte 4 Stays the Same 3
Add Insn 4
Substitute Add 4
Pc 4
Byte 1 Stays the Same 4
Byte 2 Stays the Same 4
Byte 4 Stays the Same 4
Byte 5 Stays the Same 4
Addi Insn 5
Pc 5
Byte 2 Stays the Same 5
Byte 4 Stays the Same 5
Byte 5 Stays the Same 5
Byte 3 Stays the Same 5
Addi Insn 6
Pc 6
Byte 1 Stays the Same 6
Byte 4 Stays the Same 6
Byte 5 Stays the Same 6
Byte 3 Stays the Same 6
Addi Insn 7
Pc 7
Byte 1 Stays the Same 7
Byte 2 Stays the Same 7
Byte 5 Stays the Same 7
Byte 3 Stays the Same 7
Truth Propagation Property 2
Beq No Branch 8
Byte 1 Stays the Same 8
Byte 2 Stays the Same 8
Byte 4 Stays the Same 8
Byte 5 Stays the Same 8
Byte 3 Stays the Same 8
Jump Help 9
Byte 1 Stays the Same 9
Byte 2 Stays the Same 9
Byte 4 Stays the Same 9
Byte 5 Stays the Same 9
Byte 3 Stays the Same 9
Add Insn 10
Substitute Add 10
Pc 10
Byte 1 Stays the Same 10
Byte 2 Stays the Same 10
Byte 4 Stays the Same 10
Byte 5 Stays the Same 10
Addi Insn 11
Pc 11
Byte 2 Stays the Same 11
Byte 4 Stays the Same 11
Byte 5 Stays the Same 11
Byte 3 Stays the Same 11
Addi Insn 12
Pc 12
Byte 1 Stays the Same 12
Byte 4 Stays the Same 12
Byte 5 Stays the Same 12
Byte 3 Stays the Same 12
Addi Insn 13
Pc 13
Byte 1 Stays the Same 13
Byte 2 Stays the Same 13
Byte 5 Stays the Same 13
Byte 3 Stays the Same 13
Beq No Branch 14
Byte 1 Stays the Same 14
Byte 2 Stays the Same 14
Byte 4 Stays the Same 14
Byte 5 Stays the Same 14
Byte 3 Stays the Same 14
Jump Help 15
Byte 1 Stays the Same 15
Byte 2 Stays the Same 15
Byte 4 Stays the Same 15
Byte 5 Stays the Same 15
Byte 3 Stays the Same 15
Add Insn 16
Substitute Add 16
Pc 16
Byte 1 Stays the Same 16
Byte 2 Stays the Same 16
Byte 4 Stays the Same 16
Byte 5 Stays the Same 16
Addi Insn 17
Pc 17
Byte 2 Stays the Same 17
Byte 4 Stays the Same 17
Byte 5 Stays the Same 17
Byte 3 Stays the Same 17
Addi Insn 18
Pc 18
Byte 1 Stays the Same 18
Byte 4 Stays the Same 18
Byte 5 Stays the Same 18
Byte 3 Stays the Same 18
Addi Insn 19
Pc 19
Byte 1 Stays the Same 19
Byte 2 Stays the Same 19
Byte 5 Stays the Same 19
Byte 3 Stays the Same 19
Beq No Branch 20
Byte 1 Stays the Same 20
Byte 2 Stays the Same 20
Byte 4 Stays the Same 20
Byte 5 Stays the Same 20
Byte 3 Stays the Same 20
Jump Help 21
Byte 1 Stays the Same 21
Byte 2 Stays the Same 21
Byte 4 Stays the Same 21
Byte 5 Stays the Same 21
Byte 3 Stays the Same 21
Add Insn 22
Substitute Add 22
Pc 22
Byte 1 Stays the Same 22
Byte 2 Stays the Same 22
Byte 4 Stays the Same 22
Byte 5 Stays the Same 22
Addi Insn 23
Pc 23
Byte 2 Stays the Same 23
Byte 4 Stays the Same 23
Byte 5 Stays the Same 23
Byte 3 Stays the Same 23
Addi Insn 24
Pc 24
Byte 1 Stays the Same 24
Byte 4 Stays the Same 24
Byte 5 Stays the Same 24
Byte 3 Stays the Same 24
Insns

Proof: Pc 12

Let's prove the following theorem:

if the following are true:
  • instruction #6 is addi dst=2 src=3 imm=0
  • the PC at time 12 = 6

then the PC at time 13 = 7

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 instruction #6 is addi dst=2 src=3 imm=0
2 the PC at time 12 = 6
Proof Table
# Claim Reason
1 the PC at time (12 + 1) = 6 + 1 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 12 = 6, then the PC at time (12 + 1) = 6 + 1
2 12 + 1 = 13 12 + 1 = 13
3 6 + 1 = 7 6 + 1 = 7
4 the PC at time (12 + 1) = the PC at time 13 if 12 + 1 = 13, then the PC at time (12 + 1) = the PC at time 13
5 the PC at time 13 = 7 if the PC at time (12 + 1) = 6 + 1 and the PC at time (12 + 1) = the PC at time 13 and 6 + 1 = 7, then the PC at time 13 = 7
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