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Proof step 21 from proof inv-write (previous step)

root.dir?, fids-cons(root, fs, ofh), ofh[fd].fid ∈ fs, fd ∈ ofh, n ≤ # buf, ofh[fd].mode = MODE_W ∨ ofh[fd].mode = MODE_RW ⊦ ∃ n1. n1 ≤ n

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
ofh[fd] = mkfh(fid, mode, m), root.dir?, fids-cons(root, fs, ofh), fd ∈ ofh, fid ∈ fs, n ≤ # buf, mode = MODE_W ∨ mode = MODE_RW ⊦ ∃ n1. n1 ≤ n

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], fid, mode, m]

Additional information

Used simplifier rules: ⊦ (fid = fh.fid ∧ mode = fh.mode) ∧ m = fh.pos ↔ fh = mkfh(fid, mode, m); (elim) Used terms: ofh[fd], fid, mode, m