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Proof step 63 from proof afs-cons-rename-file-dentry (previous step)

# links(entries0[str], dirs0) = m11 + 1, (m = m0 ⊃ mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0);mkdir(m4, md6, # links(m, dirs0), m8, entries0)) = mkdir(m6, md5, m9, m10, entries), dirs0[m] = mkdir(m4, md6, # links(m, dirs0), m8, entries0), files0[entries0[str]] = mkfile(m5, md0, # links(entries0[str], dirs0), content1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs = dirs0[m0, mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0)][m, mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])], files = files0[entries0[str], mkfile(m5, md0, m11, content1)], afs-cons(dirs0, files0), str0 ∈ entries1, m ∈ dirs0, m0 ∈ dirs0, entries0[str] ∈ files0, entries1[str0] ∈ files0, str ∈ entries0, 1 ≤ # links(entries0[str], dirs0), m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m0, md2, true, # links(m0, dirs0), m7, m3 + 1); dirs, files); afs_inode_sync#(mkinode(m, md1, true, # links(m, dirs0), m8, m4); dirs, files); if true then {afs_inode_sync#(mkinode(entries0[str], md, false, # links(entries0[str], dirs0), 0, m2); dirs, files); new_child_inode := getinode(entries0[str], dirs, files)}; old_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), # links(entries0[str], dirs0) = 0, entries0[str] ∈ dirs0, entries1[str0] ∈ dirs0, m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
# links(entries0[str], dirs0) = m11 + 1, (m = m0 ⊃ mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0);mkdir(m4, md6, # links(m, dirs0), m8, entries0)) = mkdir(m6, md5, m9, m10, entries), dirs0[m] = mkdir(m4, md6, # links(m, dirs0), m8, entries0), files0[entries0[str]] = mkfile(m5, md0, m11 + 1, content1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs = dirs0[m0, mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0)][m, mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])], files = files0[entries0[str], mkfile(m5, md0, m11, content1)], afs-cons(dirs0, files0), str0 ∈ entries1, m ∈ dirs0, m0 ∈ dirs0, entries0[str] ∈ files0, entries1[str0] ∈ files0, str ∈ entries0, ¬ entries0[str] ∈ dirs0, ¬ entries1[str0] ∈ dirs0, m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m0, md2, true, # links(m0, dirs0), m7, m3 + 1); dirs, files); afs_inode_sync#(mkinode(m, md1, true, # links(m, dirs0), m8, m4); dirs, files); if true then {afs_inode_sync#(mkinode(entries0[str], md, false, # links(entries0[str], dirs0), 0, m2); dirs, files); new_child_inode := getinode(entries0[str], dirs, files)}; old_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0])

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base