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Proof step 1 from proof abs-dnode-emp (conclusion)

⊦ abs(dnode(md, ∅), ino) = _∃(λ m, m0. ino => mkdir(0, md, m, m0, ∅))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ abs(dnode(md, sdt), ino) = _∃(λ ad. ino => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ )
Proof step 3:
⊦ abs(∅, entries) = (⌜entries = ∅⌝ ∧ emp)
Proof step 4:
⊦ _∃(λ ad. (⌜ad.entries = ∅⌝ ∧ ino => ad) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ ) = _∃(λ m, m0. ino => mkdir(0, md, m, m0, ∅))

Rule argument

Additional information

Used simplifier rules: abs-dnode: ⊦ abs(dnode(md, sdt), ino) = _∃ (λ ad. ino => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ );%abs-empty: ⊦ abs(∅, entries) = (⌜entries = ∅⌝ ∧ emp);%and-com: ⊦ (D ∧ D0) = (D0 ∧ D); from specification heap-sep[dir-heap]%and-ass: ⊦ ((D ∧ D0) ∧ D1) = (D ∧ D0 ∧ D1); from specification heap-sep[dir-heap]%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]% ⊦ emp * D = D; (s)% ⊦ (⌜bv⌝ ∧ D) * D0 = (⌜bv⌝ ∧ D * D0); (s)