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Proof step 34 from proof refine-close (previous step)

of[fd] = mkfile(m, mode, m0), err = ESUCCESS, fs = abs-files(files), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), fd ∈ of, psynced → asynced ⊦ [vfs_put_inode#(mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size), of -- fd, asynced; err, dirs, files)] ( of-cons(of -- fd, dirs, files) ∧ afs-cons(dirs, files) → ⟨ofh := abs-of(of); posix_close#(fd, user, root; err0, fs, ofh)⟩ (ofh = abs-of(of -- fd) ∧ fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), err = ESUCCESS, fs = abs-files(files), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), fd ∈ of, psynced → asynced ⊦ [vfs_put_inode#(mkinode(m, md, false, m2, 0, m1), of -- fd, asynced; err, dirs, files)] ( of-cons(of -- fd, dirs, files) ∧ afs-cons(dirs, files) → ⟨ofh := abs-of(of); posix_close#(fd, user, root; err0, fs, ofh)⟩ (ofh = abs-of(of -- fd) ∧ fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m], m1, md, m2, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m], m1, md, m2, content