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Proof step 8 from proof reachless-edge (previous step)

reach<(source, a, n0), b ∈ succ(a) ⊦ succ(a) = ∅, # succ(a) = 0, ∃ m. ¬ n0 < m ∧ reach(source, b, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ reach<(a, b, n) ↔ (∃ m. m < n ∧ reach(a, b, m))
Proof step 7:
∃ m. m < n0 ∧ reach(source, a, m), b ∈ succ(a) ⊦ succ(a) = ∅, # succ(a) = 0, ∃ m. ¬ n0 < m ∧ reach(source, b, m)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: reachls-def antecedent: succedent: reach<(a, b, n) ↔ (∃ m. m < n ∧ reach(a, b, m)) substlist: [n, b, a] → [n0, a, source] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (n0, a, source)]]