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Proof step 7 from proof INVR-nextlevel (previous step)

reachS(source, N, n + 1), reach(b, dest, n0 - n - 1), b ∈ N, n < n0, reach(source, dest, n0), ∀ a. ¬ a ∈ N ∨ ¬ reach(a, dest, n0 - n + 1) ∨ reach<(a, dest, n0 - n + 1) ⊦ N = ∅, # N = 0, reach<(b, dest, n0 - n - 1), reach<(source, dest, n0), ∃ 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 6:
n0 = n1 + n ∧ n ≤ n0, reachS(source, N, n + 1), reach(b, dest, n1 - 1), b ∈ N, n < n0, reach(source, dest, n0), ∀ a. ¬ a ∈ N ∨ ¬ reach(a, dest, n0 - n + 1) ∨ reach<(a, dest, n0 - n + 1) ⊦ N = ∅, # N = 0, reach<(b, dest, n1 - 1), reach<(source, dest, n0), ∃ 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-sub antecedent: n ≤ m succedent: n0 = m - n ↔ m = n0 + n substlist: [m, n, n0] → [n0, n, n1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m < n → ¬ n < m], [CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (n0, n, n1)]]