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Proof step 22 from proof cyclic-weak-def (previous step)

x = r + x1 ∧ x ≠ [], # x = 2 + # H, path(x, 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 21:
# x1 = 1 + # H, path(r ' + x1, H), ∀ n. ∃ r0. reachable-n(H, n, r, r0) ⊦ cyclic(r, H)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' + x0 ≠ []], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : n < n0 ⊦ m + ((* n)) = m0 + ((* n0)) ↔ m = m0 + (n0 - n)], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (x0 + x1) = # x0 + # x1], [CSIMPSEQ : ⊦ r + x0 = r ' + x0])]]