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Proof step 5 from proof INVR-nextlevel (previous step)

reach(source, dest, n1 + n), reachS(source, N, n + 1), reach(b, dest, n1 - 1), b ∈ N, ∀ a. ¬ a ∈ N ∨ ¬ reach(a, dest, n1 - 1) ∨ reach<(a, dest, n1 - 1) ⊦ N = ∅, # N = 0, n1 = 0, reach<(b, dest, n1 - 1), reach<(source, dest, n1 + n), ∃ b0. ¬ ((∃ c. reach(source, c, n) ∧ b0 ∈ succ(c)) ∧ ¬ reach<(source, b0, n + 1) → b0 ∈ N), ∃ b0. ¬ (b0 ∈ V ↔ reach<(source, b0, n + 1) ∨ (∃ a. b0 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
n1 = m + 1, reach(source, dest, n1 + n), reachS(source, N, n + 1), reach(b, dest, m), b ∈ N, ∀ a. ¬ a ∈ N ∨ ¬ reach(a, dest, m) ∨ reach<(a, dest, m) ⊦ N = ∅, # N = 0, n1 = 0, reach<(b, dest, m), reach<(source, dest, n1 + n), ∃ b0. ¬ ((∃ c. reach(source, c, n) ∧ b0 ∈ succ(c)) ∧ ¬ reach<(source, b0, n + 1) → b0 ∈ N), ∃ b0. ¬ (b0 ∈ V ↔ reach<(source, b0, n + 1) ∨ (∃ a. b0 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)))

Rule argument

[x0lemmaarg: spec-name: nat instance-name: lemma-name: elim-pred-c antecedent: n ≠ 0 succedent: m = n - 1 ↔ n = m + 1 substlist: [n, m] → [n1, m] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1])], [EXTRATERMS : (n1, m)]]