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Proof step 181 from proof refine-writemeta (previous step)

(ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ) = mkinode(m, md0, boolvar, m0, m1, m2), root[path].dir? ↔ ino1 ∈ dirs, 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, ino1, dirs, files), of-cons(of, dirs, files), pw(user, path, root, fs), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ pw(user, md0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 182:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (pw(user, p, tree, abs-files(files)) ↔ pw(user, meta(ε, m, dirs, files)))
Proof step 183:
(ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ) = mkinode(m, md0, boolvar, m0, m1, m2), root[path].dir? ↔ ino1 ∈ dirs, 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), pw(user, meta(ε, ino1, dirs, files)), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ pw(user, md0)

Rule argument

Additional information

Used simplifier rules: pw: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( pw(user, p, tree, abs-files(files)) ↔ pw(user, meta(ε, m, dirs, files)));