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Proof step 43 from proof abs-acyclic (previous step)

entries[str] = ROOT_INO, tree[p] = dnode(md0, sdt), (( ino => mkdir(# entries, md0, # links(ino, dirs), m2, entries) * ( abs(sdt -- str, entries -- str) * _∃(λ ad. ROOT_INO => ad * abs(sdt[str].entries, ad.entries) ∧ ⌜ad.meta = sdt[str].meta⌝ ∧ ⌜ad.size = # ad.entries⌝ )) * abs|(tree, ROOT_INO, p, ino)) )(dirs), sdt[str].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, str ∈ sdt ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
ad.meta = sdt[str].meta, ad.size = # ad.entries, entries[str] = ROOT_INO, tree[p] = dnode(md0, sdt), (( ( ((ROOT_INO => ad * abs(sdt[str].entries, ad.entries)) * ino => mkdir(# entries, md0, # links(ino, dirs), m2, entries)) * abs(sdt -- str, entries -- str)) * abs|(tree, ROOT_INO, p, ino)) )(dirs), sdt[str].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, str ∈ sdt ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ((ino => ad * D))(dirs) → ino ∈ dirs; (s)%path-in-dirs: p ≠ ε ⊦ ispath(p, n, m, dirs, files) → n ∈ dirs; (forward) from specification afs-base% ⊦ ¬ false(dirs); (s)% ⊦ false * D = false; (s)% ⊦ ino => ad * ino => ad0 = false; (s)% ⊦ emp * D = D; (s)% ⊦ abs|(tree, ino, ε, ino0) = (emp ∧ ⌜ino = ino0⌝ ); (s)% ⊦ tree[ε] = tree; (s)% ⊦ ⌜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)