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Theorem base for Specification directory-tree-inst

This is a listing of all goals defined over the current specification. Axioms are marked yellow, proved theorems green and unproved theorems blue. Click on individual names to get more information on the proof.

Name: Sequent: Type:
Uniform-storePentries-tree(∅), ∀ sdt, str, tree. Pentries-tree(sdt) → Pentries-tree(sdt[str, tree]) ⊦ ∀ sdt. Pentries-tree(sdt) A Proof Obligation
Del-empty ⊦ ∅ -- str = ∅ A Proof Obligation
Del-rec-same ⊦ sdt[str, tree] -- str = sdt -- str A Proof Obligation
Del-rec-other ⊦ str ≠ str0 → sdt[str0, tree] -- str = (sdt -- str)[str0, tree] A Proof Obligation
ax ⊦ str × tree = str2 × tree0 ↔ str = str2 ∧ tree = tree0 A User Theorem
read-notin ⊦ ¬ str ∈ sdt → sdt[str] = (∅)[str] A User Theorem