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Proof step 10 from proof inv-close (previous step)

root.dir?, fids-cons(root, fs, ofh0), fd ∈ ofh0 ⊦ ⟪if ¬ ofh0[fd].fid ∈ (ofh0 -- fd).fids ∧ ¬ ofh0[fd].fid ∈ root.fids then fs := fs -- ofh0[fd].fid⟫ fids-cons(root, fs, ofh0 -- fd)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
ofh0[fd] = mkfh(fid, mode, m), root.dir?, fids-cons(root, fs, ofh0), fd ∈ ofh0 ⊦ ⟪if ¬ fid ∈ (ofh0 -- fd).fids ∧ ¬ fid ∈ root.fids then fs := fs -- fid⟫ fids-cons(root, fs, ofh0 -- fd)

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[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: ofh0[fd], fid, mode, m