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Proof step 54 from proof refine-seek (previous step)

of[fd] = mkfile(m, mode, m0), n = files[m].size + n0, ofh = abs-of(of), 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 ⊦ ⟨posix_seek#(fd, SEEK_END, user, root, abs-files(files); n0, err0, ofh)⟩ (ofh = abs-of(of[fd, of[fd].pos:= n0]) ∧ (psynced → asynced) ∧ n = n0 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), n = m1 + n0, ofh = abs-of(of), 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 ⊦ ⟨posix_seek#(fd, SEEK_END, user, root, abs-files(files); n0, err0, ofh)⟩ (ofh = abs-of(of[fd, of[fd].pos:= n0]) ∧ (psynced → asynced) ∧ n = n0 ∧ ESUCCESS = 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