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Proof step 9 from proof inv-close (previous step)

err = ESUCCESS, err0 = err1, fid = ofh0[fd].fid, ofh = ofh0 -- fd, root.dir?, fids-cons(root, fs, ofh0), pre-close(fd, err, user, root, fs, ofh0), fd ∈ ofh0 ⊦ ⟪if ¬ fid ∈ ofh.fids ∧ ¬ fid ∈ root.fids then fs := fs -- fid⟫ fids-cons(root, fs, ofh)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
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)

Rule argument

Additional information

Used simplifier rules: ⊦ pre-close(fd, ESUCCESS, user, root, fs, ofh) ↔ fd ∈ ofh; (s)