Proof Examples

2 + 2
3 + 1           (rule 2)
4 + 0           (rule 2)
4               (rule 1)
4 + 0           (rule 1)
3 + 1           (rule 2)
2 + 2           (rule 2)
(2 + 0) + 2     (rule 1)
(1 + 1) + 2     (rule 2)
(0 + 2) + 2     (rule 2)
(2 * 0 + 2) + 2 (rule 3)
2 * 1 + 2       (rule 4)
2 * 2           (rule 4)


1 + 2
2 + 1 (rule 2)
3 + 0 (rule 2)
3     (rule 1)


2 + 2
3 + 1           (rule 2)
4 + 0           (rule 2)
4               (rule 1)
4 + 0           (rule 1)
3 + 1           (rule 2)
2 + 2           (rule 2)
(2 + 0) + 2     (rule 1)
(1 + 1) + 2     (rule 2)
(0 + 2) + 2     (rule 2)
(2 * 0 + 2) + 2 (rule 3)
2 * 1 + 2       (rule 4)
2 * 2           (rule 4)
2 * (2 + 0)     (rule 1)
2 * (1 + 1)     (rule 2)