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Proof step 60 from proof path-equiv-reach (conclusion)

⊦ reach(a, b, n) ↔ (∃ x. path(x) ∧ # x = n + 1 ∧ x .first = a ∧ x .last = b)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 8:
⊦ reach(a, b, 0) ↔ (∃ x. path(x) ∧ # x = 0 + 1 ∧ x .first = a ∧ x .last = b)
Proof step 59:
∀ a, b. reach(a, b, n0) ↔ (∃ x. path(x) ∧ # x = n0 + 1 ∧ x .first = a ∧ x .last = b) ⊦ reach(a, b, n0 +1) ↔ (∃ x. path(x) ∧ # x = n0 +1 + 1 ∧ x .first = a ∧ x .last = b)

Rule argument

[term-arg: n]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;])]]