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Proof step 52 from proof abs-acyclic (previous step)

dnode(md1, sdt1)[p] = dnode(md0, sdt), entries[str] = ROOT_INO, sdt[str] = dnode(md, sdt0), (( ( ( (ROOT_INO => mkdir(# entries0, md, m0, m1, entries0) * abs(sdt0, entries0)) * ino => mkdir(# entries, md0, # links(ino, dirs), m2, entries)) * abs(sdt -- str, entries -- str)) * abs|(dnode(md1, sdt1), ROOT_INO, p, ino)) )(dirs), abs(dnode(md1, sdt1), ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(dnode(md1, sdt1), abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), str ∈ sdt, str ∈ entries ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: vfs-abs name: absc-dnode seq: ⊦ p ≠ ε → abs|(dnode(md, sdt), ino, p, ino0) = _∃ (λ ad. ino => ad * abs|(sdt, ad.entries, p, ino0) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ ) subst: [ino0, p, ino, sdt, md] → [ino, p, ROOT_INO, sdt1, md1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ((_∃ adD * D))(dirs) ↔ (∃ ad. ((adD(ad) * D))(dirs)); (s)% ⊦ (⌜bv⌝ ∧ D) * D0 = (⌜bv⌝ ∧ D * D0); (s)% ⊦ ino => ad * ino => ad0 = false; (s)% ⊦ false * D = false; (s)%sep-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]% ⊦ (false ∧ D) = false; (s)%and-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]% ⊦ ¬ false(dirs); (s)% ⊦ tree[ε] = tree; (s)% ⊦ dnode(md, sdt) = dnode(md0, sdt0) ↔ md = md0 ∧ sdt = sdt0; (ws)% ⊦ ispath(ε, n, m, dirs, files) ↔ valid-ino(n, dirs, files) ∧ m = n; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ ((ino => ad * D))(dirs) → ino ∈ dirs; (s)% ⊦ abs|(tree, ino, ε, ino0) = (emp ∧ ⌜ino = ino0⌝ ); (s)% ⊦ ⌜true⌝ = true; (s)% ⊦ (true ∧ D) = D; (s)% ⊦ emp * D = D; (s) Used terms: ino, p, ROOT_INO, sdt1, md1