Commutative Property Variation 1

Transitive Property of Equality Variation 2

Addi Zero Insn 0

Transitive Property Application 2

Addi Zero Insn 1

Byte 1 Stays the Same 1

Addi Zero Insn 2

Byte 1 Stays the Same 2

Byte 2 Stays the Same 2

Addi Zero Insn 3

Byte 1 Stays the Same 3

Byte 2 Stays the Same 3

Byte 4 Stays the Same 3

Substitute Add 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

Byte 2 Stays the Same 5

Byte 4 Stays the Same 5

Byte 5 Stays the Same 5

Byte 3 Stays the Same 5

Byte 1 Stays the Same 6

Byte 4 Stays the Same 6

Byte 5 Stays the Same 6

Byte 3 Stays the Same 6

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

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

Substitute Add 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

Byte 2 Stays the Same 11

Byte 4 Stays the Same 11

Byte 5 Stays the Same 11

Byte 3 Stays the Same 11

Byte 1 Stays the Same 12

Byte 4 Stays the Same 12

Byte 5 Stays the Same 12

Byte 3 Stays the Same 12

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

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

Substitute Add 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

Byte 2 Stays the Same 17

Byte 4 Stays the Same 17

Byte 5 Stays the Same 17

Byte 3 Stays the Same 17

Byte 1 Stays the Same 18

Byte 4 Stays the Same 18

Byte 5 Stays the Same 18

Byte 3 Stays the Same 18

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

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

Substitute Add 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

Byte 2 Stays the Same 23

Byte 4 Stays the Same 23

Byte 5 Stays the Same 23

Byte 3 Stays the Same 23

Byte 1 Stays the Same 24

Byte 4 Stays the Same 24

Byte 5 Stays the Same 24

Byte 3 Stays the Same 24

Proof: Pc 7

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 7 = 7

then the PC at time 8 = 8

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 #7 is `addi dst=4 src=4 imm=1`
2	the PC at time 7 = 7

Proof Table

#	Claim	Reason
1	the PC at time (7 + 1) = 7 + 1	if instruction #7 is `addi dst=4 src=4 imm=1` and the PC at time 7 = 7, then the PC at time (7 + 1) = 7 + 1 (Program Counter on ADDI)
2	7 + 1 = 8	7 + 1 = 8 (Fixed Value Statement)
3	the PC at time (7 + 1) = the PC at time 8	if 7 + 1 = 8, then the PC at time (7 + 1) = the PC at time 8 (Substitution)
4	the PC at time 8 = 8	if the PC at time (7 + 1) = 7 + 1 and the PC at time (7 + 1) = the PC at time 8 and 7 + 1 = 8, then the PC at time 8 = 8 (Transitive Property Application 2)

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