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Proof step 55 from proof challenge3 (conclusion)

r ≠ null, (tr(r, t) * P)(H), bst(t) ⊦ 〈search_tree_delete_min(; a, r, H)〉 ((tr(r, t .butleftmost) * P * true)(H) ∧ bst(t .butleftmost) ∧ a = t .leftmost ∧ ¬ a ∈ t .butleftmost ∧ (∀ b. b ∈ t .butleftmost → a < b))

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
r ≠ null, (tr(r, t) * P)(H) ⊦ 〈search_tree_delete_min(; a, r, H)〉 ((tr(r, t .butleftmost) * P * true)(H) ∧ a = t .leftmost)
Proof step 54:
〈search_tree_delete_min(; a, r, H)〉 ((tr(r, t .butleftmost) * P * true)(H) ∧ a = t .leftmost), r ≠ null, (tr(r, t) * P)(H), bst(t) ⊦ 〈search_tree_delete_min(; a, r, H)〉 ((tr(r, t .butleftmost) * P * true)(H) ∧ bst(t .butleftmost) ∧ a = t .leftmost ∧ ¬ a ∈ t .butleftmost ∧ (∀ b. b ∈ t .butleftmost → a < b))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: program+leftmost antecedent: r ≠ null, (tr(r, t) * P)(H) succedent: 〈search_tree_delete_min(; a, r, H)〉 ( (tr(r, t .butleftmost) * P * true)(H) ∧ a = t .leftmost) substlist: [r, t, P, H, a] → [r, t, P, H, a] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, t, P, H, a)]]