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Proof step 3 from proof legal-nxt-1 (previous step)

legal(H), r ∈ H ⊦ H[r] .nxt = null, H[r] .nxt ∈ H

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ legal(H) ↔ (∀ r. r ∈ H ∧ H[r] .nxt ≠ null → H[r] .nxt ∈ H)
Proof step 2:
∀ r. r ∈ H ∧ H[r] .nxt ≠ null → H[r] .nxt ∈ H, r ∈ H ⊦ H[r] .nxt = null, H[r] .nxt ∈ H

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: legal-def antecedent: succedent: legal(H) ↔ (∀ r. r ∈ H ∧ H[r] .nxt ≠ null → H[r] .nxt ∈ H) substlist: [H] → [H] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H)]]