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Proof step 39 from proof inv-close (previous step)

ofh0[fd] = mkfh(fid, mode, m), root.dir?, fids-cons(root, fs, ofh0), fd ∈ ofh0, n ∈ ofh0 ⊦ # (ofh0 -- fd).fids = 0, (ofh0 -- fd).fids = ∅, n = fd, ofh0[n].fid ∈ root.fids, ofh0[n].fid ∈ ofh0.fids, ofh0[n].fid ∈ fs, ¬ fid ∈ (ofh0 -- fd).fids ∧ ¬ fid ∈ root.fids

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: file-handle name: elim seq: ⊦ (fid = fh.fid ∧ mode = fh.mode) ∧ m = fh.pos ↔ fh = mkfh(fid, mode, m) subst: [fh, fid, mode, m] → [ofh0[n], fid0, mode0, m0]

Additional information

Used simplifier rules: fid-in-fs: ⊦ fids-cons(root, fs, ofh) ∧ fd ∈ ofh ∧ ofh[fd] = mkfh(fid, mode, m) → fid ∈ fs;%⊦ (fid = fh.fid ∧ mode = fh.mode) ∧ m = fh.pos ↔ fh = mkfh(fid, mode, m); (elim) Used terms: ofh0[n], fid0, mode0, m0