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Proof step 15 from proof INV-nextlevel (previous step)

reachS(source, N, n + 1), reach(source, b, m), m < 2 + n ⊦ reach<(source, b, n + 1), b ∈ V, ∃ a. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n), ∃ b1. ¬ ((∃ c. reach(source, c, n) ∧ b1 ∈ succ(c)) ∧ ¬ reach<(source, b1, n + 1) → b1 ∈ N), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ reach<(a, b, n) ↔ (∃ m. m < n ∧ reach(a, b, m))
Proof step 14:
reachS(source, N, n + 1), reach(source, b, m), m < 2 + n ⊦ ∃ m. m < n + 1 ∧ reach(source, b, m), b ∈ V, ∃ a. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n), ∃ b1. ¬ ((∃ c. reach(source, c, n) ∧ b1 ∈ succ(c)) ∧ ¬ reach<(source, b1, n + 1) → b1 ∈ N), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)))

Rule argument

[x0lemmaarg: spec-name: graph instance-name: lemma-name: reachls-def antecedent: succedent: reach<(a, b, n) ↔ (∃ m. m < n ∧ reach(a, b, m)) substlist: [n, b, a] → [n + 1, b, source] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (n + 1, b, source)]]