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Proof step 14 from proof abs-acyclic (previous step)

dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m0, entries), entries[str] = ROOT_INO, (( abs|(tree, ROOT_INO, p, ino0) * _∃(λ ad. ino0 => ad * abs(tree[p].entries, ad.entries) ∧ ⌜ad.meta = tree[p].meta⌝ ∧ ⌜ad.size = # ad.entries⌝ )) )(dirs), tree[p].dir?, abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), str ∈ entries, ino ∈ dirs ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
ad.meta = tree[p].meta, ad.size = # ad.entries, entries[str] = ROOT_INO, dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m0, entries), (((ino0 => ad * abs(tree[p].entries, ad.entries)) * abs|(tree, ROOT_INO, p, ino0)))(dirs), tree[p].dir?, abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), ino ∈ dirs, str ∈ entries ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜bv⌝ (dirs) ↔ bv; (s)% ⊦ ((D ∧ D0))(dirs) ↔ D(dirs) ∧ D0(dirs); (s)%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]%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]% ⊦ (⌜bv⌝ ∧ D) * D0 = (⌜bv⌝ ∧ D * D0); (s)% ⊦ ((_∃ adD * D))(dirs) ↔ (∃ ad. ((adD(ad) * D))(dirs)); (s)