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Proof step 70 from proof refine-fsync (previous step)

# links(ino1, dirs) = files[ino1].nlink, files[ino1] = mkfile(m, md, files[ino1].nlink, content), 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, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino1 ∈ files, ¬ root[path].dir?, ¬ ino1 ∈ dirs, psynced → asynced ⊦ [fail_or_success#(; ; err); choose bv with true in asynced := bv; if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)] ⟨posix_fsync#(path, isdir0, user, root, abs-files(files), abs-of(of); ; psynced, err0)⟩ ((psynced → asynced) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 71:
# links(ino1, dirs) = m1, files[ino1] = mkfile(m, md, m1, content), files[ino1] = mkfile(m0, md0, m1, content0), 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, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ files, ROOT_INO ∈ dirs, psynced → asynced ⊦ [fail_or_success#(; ; err); choose bv with true in asynced := bv; if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)] ⟨posix_fsync#(path, isdir0, user, root, abs-files(files), abs-of(of); ; psynced, err0)⟩ ((psynced → asynced) ∧ err = err0), root[path].dir?, ino1 ∈ 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[ino1], m0, md0, m1, content0]

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[ino1], m0, md0, m1, content0