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Proof step 16 from proof legal-noncylic-equiv-reaches-null (previous step)

# x = n0 + 1, legal(H), hd x ∈ H, path(x, H) ⊦ H[x .last] .nxt = null, hd x = null, n0 = 0, ∃ r0. reachable(hd x, r0, H) ∧ H[r0] .nxt = null, x .last ≠ null ∧ x .last ∈ H

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
x = r + x1 ∧ x ≠ [], # x = n0 + 1, legal(H), r ∈ H, path(x, H) ⊦ H[x .last] .nxt = null, r = null, n0 = 0, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, x .last ≠ null ∧ x .last ∈ H

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: reflist lemma-name: elim-list-c antecedent: x0 ≠ [] succedent: r = hd x0 ∧ x1 = tl x0 ↔ x0 = r + x1 substlist: [x0, r, x1] → [x, r, x0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPELIM : x0 ≠ [] ⊦ r = hd x0 ∧ x1 = tl x0 ↔ x0 = r + x1])], [EXTRATERMS : (x, r, x0)]]