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Proof step 12 from proof reach-rec-rev (previous step)

b ∈ succ(c), c ∈ succ(c0), reach(a, c0, n0), reach(a, b, 2 + n0), (∃ c0. reach(a, c0, n0) ∧ c ∈ succ(c0)) → (∃ c0. c0 ∈ succ(a) ∧ reach(c0, c, n0)) ⊦ succ(c) = ∅, succ(c0) = ∅, # succ(c) = 0, # succ(c0) = 0, ∃ c. c ∈ succ(a) ∧ (∃ c0. reach(c, c0, n0) ∧ b ∈ succ(c0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
b ∈ succ(c), c ∈ succ(c0), reach(a, c0, n0), reach(a, b, 2 + n0), (∃ c0. reach(a, c0, n0) ∧ c ∈ succ(c0)) → c1 ∈ succ(a) ∧ reach(c1, c, n0) ⊦ succ(c) = ∅, succ(c0) = ∅, # succ(c) = 0, # succ(c0) = 0, ∃ c. c ∈ succ(a) ∧ (∃ c0. reach(c, c0, n0) ∧ b ∈ succ(c0))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]