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Proof step 89 from proof refine-writemeta (previous step)

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)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pw(user, files[m].meta), px-parent(user, path, ROOT_INO, dirs, files), m ∈ files, ¬ root[path].dir?, ¬ m ∈ dirs, psynced → asynced0 ⊦ ⟨posix_writemeta#(path, md, user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files[m, (files[m].meta:= md).size:= files[m].size]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 90:
files[m] = mkfile(m0, md0, m1, content), 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)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files), m ∈ files, psynced → asynced0 ⊦ ⟨posix_writemeta#(path, md, user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files[m, (files[m].meta:= md).size:= m0]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err1), root[path].dir?, m ∈ dirs

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], m0, md0, m1, 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], m0, md0, m1, content