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Proof step 249 from proof refine-readmeta (previous step)

root[path].dir? ↔ ino2 ∈ dirs, ino0 = ino3, ino1 = ino4, md = md0, root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ¬ pr (user, (ino2 ∈ dirs ⊃ mkinode(ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode(ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ) .meta), psynced → asynced, ino2 ∈ dirs ∨ ino2 ∈ files ⊦ ⟨posix_readmeta#(path, user, root, abs-files(files), abs-of(of); md0, ino4, ino3, err0)⟩ ((psynced → asynced) ∧ md = md0 ∧ ino1 = ino4 ∧ ino0 = ino3 ∧ EACCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 250:
(ino2 ∈ dirs ⊃ mkinode(ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode(ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ) = mkinode(m, md1, boolvar, m0, m1, m2), root[path].dir? ↔ ino2 ∈ dirs, ino0 = ino3, ino1 = ino4, md = md0, root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced, ino2 ∈ dirs ∨ ino2 ∈ files ⊦ ⟨posix_readmeta#(path, user, root, abs-files(files), abs-of(of); md0, ino4, ino3, err0)⟩ ((psynced → asynced) ∧ md = md0 ∧ ino1 = ino4 ∧ ino0 = ino3 ∧ EACCESS = err0), pr(user, md1)

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [(ino2 ∈ dirs ⊃ mkinode (ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode (ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ), m, md1, boolvar, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: (ino2 ∈ dirs ⊃ mkinode (ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode (ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ), m, md1, boolvar, m0, m1, m2