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Proof step 20 from proof cyclic-weak-def (previous step)

path(r ' + x1, H) ∧ dups(r ' + x1) → cyclic(hd (r ' + x1), H), # x1 = 1 + # H, path(r ' + x1, H), ∀ n. ∃ r0. reachable-n(H, n, r, r0) ⊦ cyclic(r, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# x1 = 1 + # H, path(r ' + x1, H), ∀ n. ∃ r0. reachable-n(H, n, r, r0) ⊦ cyclic(r, H), r ∈ x1, dups(x1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ hd (r ' + x0) = r], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ dups(r ' + x0) ↔ ¬ ¬ (r ∈ x0 ∨ dups(x0))])]]