Proof: Substitute Add 4
Let's prove the following theorem:
if the following are true:
- value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4)
- value of cell 1 at time 4 = 0
- value of cell 2 at time 4 = 1
then value of cell 3 at time 5 = 1
Proof:
Given
1 | value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4) |
---|---|
2 | value of cell 1 at time 4 = 0 |
3 | value of cell 2 at time 4 = 1 |
# | Claim | Reason |
---|---|---|
1 | (value of cell 1 at time 4) + (value of cell 2 at time 4) = 0 + (value of cell 2 at time 4) | if value of cell 1 at time 4 = 0, then (value of cell 1 at time 4) + (value of cell 2 at time 4) = 0 + (value of cell 2 at time 4) |
2 | value of cell 3 at time 5 = 0 + (value of cell 2 at time 4) | if value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4) and (value of cell 1 at time 4) + (value of cell 2 at time 4) = 0 + (value of cell 2 at time 4), then value of cell 3 at time 5 = 0 + (value of cell 2 at time 4) |
3 | 0 + (value of cell 2 at time 4) = 0 + 1 | if value of cell 2 at time 4 = 1, then 0 + (value of cell 2 at time 4) = 0 + 1 |
4 | value of cell 3 at time 5 = 0 + 1 | if value of cell 3 at time 5 = 0 + (value of cell 2 at time 4) and 0 + (value of cell 2 at time 4) = 0 + 1, then value of cell 3 at time 5 = 0 + 1 |
5 | 0 + 1 = 1 | 0 + 1 = 1 |
6 | value of cell 3 at time 5 = 1 | if value of cell 3 at time 5 = 0 + 1 and 0 + 1 = 1, then value of cell 3 at time 5 = 1 |
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