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Proof step 27 from proof inv-close (previous step)

ofh0[fd] = mkfh(fid, mode, m), ofh0[n] = mkfh(fid0, mode0, m0), root.dir?, fids-cons(root, fs, ofh0), fid0 ∈ fs, fd ∈ ofh0, n ∈ ofh0 ⊦ # ofh0.fids = 0, ofh0.fids = ∅, fid0 = fid, fid ∈ root.fids, fid ∈ (ofh0 -- fd).fids, fid0 ∈ root.fids, fid0 ∈ (ofh0 -- fd).fids

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ fid ∈ ofh.fids ↔ (∃ n. n ∈ ofh ∧ ofh[n].fid = fid)
Proof step 29:
ofh0[n] = mkfh(fid0, mode0, m0), ofh0[fd] = mkfh(fid, mode, m), root.dir?, fids-cons(root, fs, ofh0), n ∈ ofh0, fd ∈ ofh0, fid0 ∈ fs ⊦ # ofh0.fids = 0, ofh0.fids = ∅, fid0 = fid, fid0 ∈ root.fids, fid ∈ (ofh0 -- fd).fids, fid ∈ root.fids, ∃ n. n ∈ ofh0 -- fd ∧ (ofh0 -- fd)[n].fid = fid0

Rule argument

spec: posix-base name: ofh-fids seq: ⊦ fid ∈ ofh.fids ↔ (∃ n. n ∈ ofh ∧ ofh[n].fid = fid) subst: [ofh, fid] → [ofh0 -- fd, fid0] flags: <all paths>

Additional information

Used terms: ofh0 -- fd, fid0