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Proof step 38 from proof abs-unshared-h (previous step)

(( ( ( ((n1 => mkdir(# entries, tree0[p0].meta, m0, m1, entries) * abs(tree0[p0].entries, entries)) * abs|(tree1, ino1, p1, n1)) * abs(tree1[p1], n1)) * abs|(tree0, ino0, p0, n1)) * D) )(dirs), tree0[p0].dir?, ispath(p1, ino1, n1, dirs, files), ispath(p0, ino0, n1, dirs, files), p1 ∈ tree1, p0 ∈ tree0, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ ∀ fid. tree1[p1] ≠ fnode(fid)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
⊦ abs(fnode(fid), ino) = (emp ∧ ⌜ino = fid.ino⌝ )
Proof step 40:
⊦ p ∈ tree ∧ ((abs|(tree, ino, p, ino0) * D))(dirs) ∧ ispath(p, ino, ino1, dirs, files) → ino0 = ino1
Proof step 41:
tree1[p1] = fnode(fid), (( ( ((fid.ino => mkdir(# entries, tree0[p0].meta, m0, m1, entries) * abs(tree0[p0].entries, entries)) * abs|(tree1, ino1, p1, fid.ino)) * abs|(tree0, ino0, p0, fid.ino)) * D) )(dirs), tree0[p0].dir?, ispath(p0, ino0, fid.ino, dirs, files), ispath(p1, ino1, fid.ino, dirs, files), p0 ∈ tree0, p1 ∈ tree1, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files ⊦

Rule argument

Additional information

Used simplifier rules: abs-fnode: ⊦ abs(fnode(fid), ino) = (emp ∧ ⌜ino = fid.ino⌝ );%absc-path: ⊦ p ∈ tree ∧ ((abs|(tree, ino, p, ino0) * D))(dirs) ∧ ispath(p, ino, ino1, dirs, files) → ino0 = ino1;% ⊦ ⌜bv⌝ (dirs) ↔ bv; (s)% ⊦ ((D ∧ D0))(dirs) ↔ D(dirs) ∧ D0(dirs); (s)%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]%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]% ⊦ emp * D = D; (s)% ⊦ (⌜bv⌝ ∧ D) * D0 = (⌜bv⌝ ∧ D * D0); (s)