[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 3 from proof abs-fold-new (previous step)

tree[p] = dnode(md, sdt), abs(tree0, ino1) = emp, ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(# entries + 1, md, m0, m1, entries[str, ino1]) * abs(sdt, entries)))(dirs), p ∈ tree ⊦ abs(tree[p + str ', tree0], ROOT_INO)(dirs), str ∈ entries

User applied rule apply lemma

And obtained the following new goals

Proof step 4:
D ⊆ abs(tree0, ino1) ⊦ ¬ str ∈ entries ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt) ∧ ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(# entries + 1, md, m0, m1, entries[str, ino1]) * abs(sdt, entries) * D))(dirs) → abs(tree[p + str ', tree0], ROOT_INO)(dirs)

Rule argument

spec: <toplevel> name: abs-fold-new-p seq: D ⊆ abs(tree0, ino1) ⊦ ¬ str ∈ entries ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt) ∧ (( abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir (# entries + 1, md, m0, m1, entries[str, ino1]) * abs(sdt, entries) * D) )(dirs) → abs(tree[p + str ', tree0], ROOT_INO)(dirs) subst: [D, tree0, ino1, str, entries, p, tree, md, sdt, ino0, m0, m1, dirs] → [emp, tree0, ino1, str, entries, p, tree, md, sdt, ino0, m0, m1, dirs]

Additional information

Used simplifier rules: ⊦ emp * D = D; (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]% ⊦ D ⊆ D; (s) Used terms: emp, tree0, ino1, str, entries, p, tree, md, sdt, ino0, m0, m1, dirs