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

reach(source, c, m), m < n, reachS(source, N, n + 1), reach(source, c, n), b ∈ succ(c) ⊦ # succ(c) = 0, succ(c) = ∅, b ∈ V, ∃ m0. ¬ n < m0 ∧ reach(source, b, m0), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ 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), ∃ a. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)

User applied rule exists right

And obtained the following new goals

Proof step 6:
reach(source, c, m), m < n, reachS(source, N, n + 1), reach(source, c, n), b ∈ succ(c) ⊦ # succ(c) = 0, succ(c) = ∅, b ∈ V, ¬ n < m + 1 ∧ reach(source, b, m + 1), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ 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), ∃ a. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)

Rule argument

[EXRARG : pos: right 4, [extquanttermlist: (m + 1)abort:F, discard:T, computed:F]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (m + 1)]]