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Proof step 74 from proof abs-nlinks-h (previous step)

tree[p] = dnode(md, sdt), (( m => mkdir(# entries, md, m1, m2, entries) * (⌜str ∈ entries⌝ ∧ abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * abs|(tree, ino0, p, m)) )(dirs), ispath(p, ino0, m, dirs, files), str ∈ entries, p ∈ tree, ino0 ∈ dirs, entries[str] ∈ files, str ∈ sdt, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ # links(entries[str], dirs) = 0, ⌜entries[str]⌝ ∈ tree.fids

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
tree[p] = dnode(md, sdt), ((m => mkdir(# entries, md, m1, m2, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * abs|(tree, ino0, p, m)))(dirs), ispath(p, ino0, m, dirs, files), str ∈ sdt, entries[str] ∈ files, ino0 ∈ dirs, p ∈ tree, str ∈ entries, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ # links(entries[str], dirs) = 0, ⌜entries[str]⌝ ∈ tree.fids

Rule argument

Additional information

Used simplifier rules: 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]% ⊦ (true ∧ D) = D; (s)% ⊦ ⌜true⌝ = true; (s)