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Proof step 16 from proof abs-tree (previous step)

(((fid.ino => mkdir(# entries, md, m0, m1, entries) * abs(sdt, entries)) * D0))(dirs), D1(dirs), ∀ ino0. ⌜ino0⌝ = fid → ino0 ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino0. ⌜ino0⌝ ∈ sdt.fids → ino0 ∈ files ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
fid = ⌜m⌝ , (((m => mkdir(# entries, md, m0, m1, entries) * abs(sdt, entries)) * D0))(dirs), D1(dirs), ∀ ino0. ⌜ino0⌝ ∈ sdt.fids → ino0 ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino0. ⌜ino0⌝ = fid → ino0 ∈ files ⊦

Rule argument

spec: file-id-data name: elim seq: ⊦ m = fid.ino ↔ fid = ⌜m⌝ subst: [fid, m] → [fid, m1]

Additional information

Used simplifier rules: ⊦ m = fid.ino ↔ fid = ⌜m⌝ ; (elim) Used terms: fid, m1