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Proof step 25 from proof abs-unshared-h (previous step)

tree0[p0] = fnode(fid), ((((abs|(tree1, ino1, p1, fid.ino) * abs(tree1[p1], fid.ino)) * abs|(tree0, ino0, p0, fid.ino)) * D))(dirs), ispath(p0, ino0, fid.ino, dirs, files), ispath(p1, ino1, fid.ino, dirs, files), p0 ∈ tree0, fid.ino ∈ dirs, p1 ∈ tree1, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
tree0[p0] = fnode(fid), fid = ⌜m⌝ , ((((abs|(tree1, ino1, p1, m) * abs(tree1[p1], m)) * abs|(tree0, ino0, p0, m)) * D))(dirs), ispath(p1, ino1, m, dirs, files), ispath(p0, ino0, m, dirs, files), p1 ∈ tree1, m ∈ dirs, p0 ∈ tree0, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦

Rule argument

spec: file-id-data name: elim seq: ⊦ m = fid.ino ↔ fid = ⌜m⌝ subst: [fid, m] → [fid, m]

Additional information

Used simplifier rules: ⊦ m = fid.ino ↔ fid = ⌜m⌝ ; (elim) Used terms: fid, m