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Proof step 8 from proof refine-insert (previous step)

bst(t), ((tr(r, t) * P))(H) ⊦ ⟪search_tree_insert(a; r, H)⟫ ⟨s := t.set; ordered_set_insert(a; s)⟩ ⟨t := t.insert(a)⟩ (s = t.set ∧ ((tr(r, t) * P))(H) ∧ bst(t))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 1:
((tr(r, t) * P))(H) ⊦ ⟪search_tree_insert(a; r, H)⟫ ((tr(r, t.insert(a)) * P))(H)

Rule argument

spec: search-tree inst: name: insert-prepost-shape seq: ((tr(r, t) * P))(H) ⊦ ⟪search_tree_insert(a; r, H)⟫ ((tr(r, t.insert(a)) * P))(H) subst: [r, t, P, H, a] → [r, t, P, H, a] flags: []

Additional information

[Concretesimprules(()), Extraterms((rtPHa))]