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Proof step 18 from proof inv-rmdir (previous step)

1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, boolvar0, dentrykeys(inodekey(fs[ri[dentrykey(m0, str)]].ino), ri) = ∅, links(fs[ri[dentrykey(m0, str)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str), m = fs[ri[dentrykey(m0, str)]].ino, m1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs[ri[inodekey(m0)]].nlink, m4 = fs[ri[inodekey(m0)]].nsubdirs, m5 = fs[ri[inodekey(m0)]].size, p_inode = mkinode(m0, md0, boolvar0, m3, m4, m5), fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].directory, ro.inodes?, fo.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(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), dentrykey(m0, str) ∈ ri, inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ri, inodekey(m0) ∈ ri, 1 ≤ m5, 1 ≤ m4, m3 ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪aubifs_core_journal_add3# (inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1), dentrynode(dentrykey(m0, str), 0), inodenode(inodekey(m), md, true, 0, m1, m2), ri, fi, ro, fo ; adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m0), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m0, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, boolvar0, m3, m4 - 1, m5 - 1).meta, inodenode(inodekey(m0), md0, boolvar0, m3, m4 - 1, m5 - 1).directory, inodenode(inodekey(m0), md0, boolvar0, m3, m4 - 1, m5 - 1).nlink, inodenode(inodekey(m0), md0, boolvar0, m3, m4 - 1, m5 - 1).nsubdirs, inodenode(inodekey(m0), md0, boolvar0, m3, m4 - 1, m5 - 1).size); c_inode0 := mkinode (m, inodenode(inodekey(m), md, true, 0, m1, m2).meta, inodenode(inodekey(m), md, true, 0, m1, m2).directory, inodenode(inodekey(m), md, true, 0, m1, m2).nlink, inodenode(inodekey(m), md, true, 0, m1, m2).nsubdirs, inodenode(inodekey(m), md, true, 0, m1, m2).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)), fs[ri[dentrykey(m0, str)]].ino = ROOT_INO, m4 = 0, m5 = 0, inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ro, inodekey(m0) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs[ri[dentrykey(m0, str)]].ino), ri) = ∅, links(fs[ri[dentrykey(m0, str)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str), m = fs[ri[dentrykey(m0, str)]].ino, m1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs[ri[inodekey(m0)]].nlink, m4 = fs[ri[inodekey(m0)]].nsubdirs, m5 = fs[ri[inodekey(m0)]].size, fs[ri[dentrykey(m0, str)]].ino ≠ ROOT_INO, fs[ri[inodekey(m0)]].nsubdirs ≠ 0, fs[ri[inodekey(m0)]].size ≠ 0, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].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), inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(m0) ∈ ri, 1 ≤ fs[ri[inodekey(m0)]].nsubdirs, 1 ≤ fs[ri[inodekey(m0)]].size, ¬ inodekey(m0) ∈ ro, ¬ inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ro, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪aubifs_core_journal_add3# (inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1), dentrynode(dentrykey(m0, str), 0), inodenode(inodekey(m), md, true, 0, m1, m2), ri, fi, ro, fo ; adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m0), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m0, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).meta, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).directory, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nlink, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nsubdirs, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).size); c_inode0 := mkinode (m, inodenode(inodekey(m), md, true, 0, m1, m2).meta, inodenode(inodekey(m), md, true, 0, m1, m2).directory, inodenode(inodekey(m), md, true, 0, m1, m2).nlink, inodenode(inodekey(m), md, true, 0, m1, m2).nsubdirs, inodenode(inodekey(m), md, true, 0, m1, m2).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))

Rule argument

Additional information

Used simplifier rules: ⊦ #(∅ ++ key) = 1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%one-size: ⊦ ks = ∅ ++ key → # ks = 1; (forward) from specification set-basic[node-index]