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Proof step 26 from proof legal-noncylic-equiv-reaches-null (previous step)

legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, reachable-n(H, n0 + 1, r, H[r0] .nxt)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0))
Proof step 25:
legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, ∃ r1. reachable-n(H, n0, r, r1) ∧ reachable-1(H, r1, H[r0] .nxt)

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reachable-n-rec-rev antecedent: succedent: reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0)) substlist: [r0, r, n, H] → [H[r0] .nxt, r, n0, H] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H[r0] .nxt, r, n0, H)]]