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Proof step 31 from proof inv-rename-overwrite-reparent (previous step)

¬ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, m10 = fs[ri[inodekey(m)]].size, m8 = fs[ri[inodekey(m)]].nlink, m9 = fs[ri[inodekey(m)]].nsubdirs, new_child_inode = mkinode(fs[ri[dentrykey(m0, str0)]].ino, md2, boolvar1, m5, m6, m7), new_dent = mkdentry(str0, fs[ri[dentrykey(m0, str0)]].ino), new_parent_inode = mkinode(m0, md0, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), fs[ri[dentrykey(m0, str0)]].ino ≠ ROOT_INO, fs[ri[inodekey(m)]].size ≠ 0, m0 ≠ m, m5 ≠ 0, fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m0)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), dentrykey(m, str) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m0, str0) ∈ ri, inodekey(fs[ri[dentrykey(m0, str0)]].ino) ∈ ri, inodekey(m) ∈ ri, inodekey(m0) ∈ ri, ri[dentrykey(m, str)] ∈ fs, 1 ≤ fs[ri[inodekey(m)]].size, (boolvar3 ⊃ 1;0) ≤ fs[ri[inodekey(m)]].nsubdirs, 1 ≤ m5, ¬ inodekey(m0) ∈ ro, ¬ inodekey(m) ∈ ro, boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, m5 = 1 → links(fs[ri[dentrykey(m0, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str0), fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m0, str0)]].ino), ri) = ∅, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar3 ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ boolvar3 ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].size ⊦ ⟪aubifs_core_journal_add5# (dentrynode(dentrykey(m, old_dent.name), 0), dentrynode(dentrykey(new_parent_inode.ino, new_dent.name), old_dent.ino), inodenode(inodekey(m), md, true, m8, m9 - (boolvar3 ⊃ 1;0), m10 - 1), inodenode (inodekey(new_parent_inode.ino), new_parent_inode.meta, new_parent_inode.directory, new_parent_inode.nlink, new_parent_inode.nsubdirs, new_parent_inode.size), inodenode (inodekey(new_dent.ino), new_child_inode.meta, new_child_inode.directory, new_child_inode.nlink - 1, new_child_inode.nsubdirs, new_child_inode.size), ri, fi, ro, fo ; adr3, adr2, adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(m, old_dent.name), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(new_parent_inode.ino, new_dent.name), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(new_parent_inode.ino), adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(new_dent.ino), adr, fi, ro, fo, fs, log, boolvar; ri); nd := inodenode (inodekey(new_dent.ino), new_child_inode.meta, new_child_inode.directory, new_child_inode.nlink - 1, new_child_inode.nsubdirs, new_child_inode.size); if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(new_dent.ino), ri, fi, fo, fs, log, boolvar; ro); new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m8, m9 - (boolvar3 ⊃ 1;0), m10 - 1).meta, inodenode(inodekey(m), md, true, m8, m9 - (boolvar3 ⊃ 1;0), m10 - 1).directory, inodenode(inodekey(m), md, true, m8, m9 - (boolvar3 ⊃ 1;0), m10 - 1).nlink, inodenode(inodekey(m), md, true, m8, m9 - (boolvar3 ⊃ 1;0), m10 - 1).nsubdirs, inodenode(inodekey(m), md, true, m8, m9 - (boolvar3 ⊃ 1;0), m10 - 1).size); new_child_inode := mkinode(new_child_inode.ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)}⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m10, m1]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m10, m1