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Proof step 18 from proof legal-noncylic-equiv-reaches-null (previous step)

legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ H[r0] .nxt = null, r = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, r0 ≠ null ∧ r0 ∈ H

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ n ≠ 0 → (reachable-n(H, n, r, r0) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x .last = r0 ∧ # x = n + 1))
Proof step 17:
n0 ≠ 0, legal(H), r ∈ H, ∃ x. path(x, H) ∧ hd x = r ∧ x .last = r0 ∧ # x = n0 + 1 ⊦ H[r0] .nxt = null, r = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, r0 ≠ null ∧ r0 ∈ H

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reach-n-path-n antecedent: succedent: n ≠ 0 → ( reachable-n(H, n, r, r0) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x .last = r0 ∧ # x = n + 1)) substlist: [r0, r, n, H] → [r0, r, n0, H] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ reachable-n(H, 0, r, r0) ↔ r = r0])], [EXTRATERMS : (r0, r, n0, H)]]