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Proof step 37 from proof inv-fsync (previous step)

⟨vfs_walk#(p, user, dirs, files, asynced; ino1, err)⟩ (ino1 = ino0 ∧ err = ESUCCESS), err = ESUCCESS, ino1 = ROOT_INO, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pr(user, files[ino0].meta), px-parent(user, p, ROOT_INO, dirs, files), ino0 ∈ files, ¬ ino0 ∈ dirs ⊦ ⟪afs_fsync#(mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size), isdir0, dirs, files; ; asynced, err); if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 38:
⟨vfs_walk#(p, user, dirs, files, asynced; ino1, err)⟩ (ino1 = ino0 ∧ err = ESUCCESS), files[ino0] = mkfile(m, md, m0, content), err = ESUCCESS, ino1 = ROOT_INO, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, p, ROOT_INO, dirs, files), ino0 ∈ files ⊦ ⟪afs_fsync#(mkinode(ino0, md, false, m0, 0, m), isdir0, dirs, files; ; asynced, err); if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)⟫ true, ino0 ∈ 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[ino0], m, md, m0, 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[ino0], m, md, m0, content