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Proof step 31 from proof abs-tree (previous step)

D0(dirs), D1(dirs), fid.ino ∈ files, ∀ ino. ⌜ino⌝ = fid → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ ⌜fid.ino⌝ = fid

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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