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Proof step 28 from proof inv-rmdir (previous step)

1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs0[ri[dentrykey(m0, str)]].ino), ri) = ∅, fs = fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs - 1, fs0[ri[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].size) ], links(fs0[ri[dentrykey(m0, str)]].ino, fs0, ri) = ∅ ++ dentrykey(m0, str), m = fs0[ri[dentrykey(m0, str)]].ino, m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs0[ri[inodekey(m0)]].nlink, m4 = fs0[ri[inodekey(m0)]].nsubdirs, m5 = fs0[ri[inodekey(m0)]].size, fs0[ri[dentrykey(m0, str)]].ino ≠ ROOT_INO, fs0[ri[dentrykey(m0, str)]].ino ≠ 0, fs0[ri[inodekey(m0)]].nsubdirs ≠ 0, fs0[ri[inodekey(m0)]].size ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m0 ≠ 0, fs0[ri[inodekey(m0)]].directory, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m0) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(fs0[ri[dentrykey(m0, str)]].ino) ∈ ri, 1 ≤ fs0[ri[inodekey(m0)]].size, 1 ≤ fs0[ri[inodekey(m0)]].nsubdirs, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ inodekey(m0) ∈ ro, ¬ inodekey(fs0[ri[dentrykey(m0, str)]].ino) ∈ ro, fs0[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪aubifs_core_index_store#(inodekey(m0), adr1, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_remove#(dentrykey(m0, str), fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', 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, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 29:
1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nlink, adr = adr1, dentrykeys(inodekey(fs0[ri[dentrykey(m0, str)]].ino), ri) = ∅, fs = fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs - 1, fs0[ri[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].size) ], key = inodekey(m0), links(fs0[ri[dentrykey(m0, str)]].ino, fs0, ri) = ∅ ++ dentrykey(m0, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', m = fs0[ri[dentrykey(m0, str)]].ino, m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs0[ri[inodekey(m0)]].nlink, m4 = fs0[ri[inodekey(m0)]].nsubdirs, m5 = fs0[ri[inodekey(m0)]].size, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].directory, fs0[ri[inodekey(m0)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(fs0[ri[dentrykey(m0, str)]].ino) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(m0) ∈ ri, 1 ≤ fs0[ri[inodekey(m0)]].nsubdirs, 1 ≤ fs0[ri[inodekey(m0)]].size, fs0[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; aubifs_core_index_remove#(dentrykey(m0, str), fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', 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, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), fs0[ri[dentrykey(m0, str)]].ino = ROOT_INO, fs0[ri[dentrykey(m0, str)]].ino = 0, fs0[ri[inodekey(m0)]].nsubdirs = 0, fs0[ri[inodekey(m0)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(fs0[ri[dentrykey(m0, str)]].ino) ∈ ro

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_index_store#(KEY, ADR, FI, RO, FO, FS, LOG, CSYNCED; RI) {if ¬ ADR ∈ RI ∧ ADR ∈ FS ∧ key-cons(KEY, FS[ADR]) then RI[KEY] := ADR else abort };