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Proof step 25 from proof inv-seek (previous step)

fid ∈ fs ↔ fid ∈ root.fids ∨ fid ∈ ofh.fids, root.dir?, fids-cons(root, fs, ofh), ofh[fd].fid ∈ fs, fd ∈ ofh ⊦ fid ∈ fs ↔ fid ∈ root.fids ∨ fid ∈ ofh[fd, mkfh(ofh[fd].fid, ofh[fd].mode, n)].fids, whence = SEEK_END, whence = SEEK_CUR

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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] → [ofh[fd], fid0, mode, m]

Additional information

Used simplifier rules: ⊦ fd ∈ ofh ∧ ofh[fd] = mkfh(fid, mode0, n0) → ofh[fd, mkfh(fid, mode1, n1)].fids = ofh.fids; (s)%⊦ (fid = fh.fid ∧ mode = fh.mode) ∧ m = fh.pos ↔ fh = mkfh(fid, mode, m); (elim) Used terms: ofh[fd], fid0, mode, m