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Proof step 49 from proof inv-rename-new-reparent (previous step)

m1 + 1 = fs0[ri[inodekey(m)]].size, n0 + (boolvar2 ⊃ 1;0) = fs0[ri[inodekey(m)]].nsubdirs, fs0[ri[dentrykey(m, str)]] = dentrynode(key, m3), fs0[ri[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), adr5 = adr7, adr6 = adr8, err = ESUCCESS, fs = fs0[adr1, nd2][adr2, nd1][adr3, nd0][adr4, nd], log = (((log0 + adr1) + adr2) + adr3) + adr4, m2 = fs0[ri[inodekey(m)]].nlink, m6 = fs0[ri[inodekey(m0)]].nlink, m7 = fs0[ri[inodekey(m0)]].nsubdirs, m8 = fs0[ri[inodekey(m0)]].size, nd = inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1), nd0 = inodenode(inodekey(m), md, true, m2, n0, m1), nd1 = dentrynode(dentrykey(m0, str0), mkdentry(str, m3).ino), nd2 = dentrynode(dentrykey(m, str), 0), mkdentry(str, m3).dentry?, fs0[ri[inodekey(m)]].directory, fs0[ri[inodekey(m0)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + adr2 ' + (adr3 ' + adr4), fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), dentrykey(m, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(m0) ∈ ri, inodekey(m) ∈ ri, ri[dentrykey(m, str)] ∈ fs0, ri[inodekey(m3)] ∈ fs0, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs0[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10 ⊦ ⟪aubifs_core_index_remove#(dentrykey(m, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(m0, str0), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m0), adr4, fi, ro, fo, fs, log, boolvar; ri); new_dent := mkdentry(str0, mkdentry(str, m3).ino); old_dent := negdentry(str); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m2, n0, m1).meta, inodenode(inodekey(m), md, true, m2, n0, m1).directory, inodenode(inodekey(m), md, true, m2, n0, m1).nlink, inodenode(inodekey(m), md, true, m2, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, m2, n0, m1).size); new_parent_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).meta, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).directory, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).nlink, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).nsubdirs, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).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)), m0 = m, dups(adr1 ' + adr2 ' + adr3 ' + adr4 '), inodekey(m) ∈ ro, dentrykey(m0, str0) ∈ ri, inodekey(m0) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
n0 + (boolvar2 ⊃ 1;0) = fs0[ri[inodekey(m)]].nsubdirs, m1 + 1 = fs0[ri[inodekey(m)]].size, fs0[ri[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), fs0[ri[dentrykey(m, str)]] = dentrynode(key, m3), fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode(inodekey(m0), md0, true, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri[inodekey(m0)]].size + 1) ], m2 = fs0[ri[inodekey(m)]].nlink, m6 = fs0[ri[inodekey(m0)]].nlink, m7 = fs0[ri[inodekey(m0)]].nsubdirs, m8 = fs0[ri[inodekey(m0)]].size, adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr2 ≠ adr3, adr2 ≠ adr4, adr3 ≠ adr4, m0 ≠ m, fs0[ri[inodekey(m0)]].directory, fs0[ri[inodekey(m)]].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-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[inodekey(m3)] ∈ fs0, ri[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri, inodekey(m0) ∈ ri, inodekey(m3) ∈ ri, dentrykey(m, str) ∈ ri, ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ inodekey(m0) ∈ ro, ¬ dentrykey(m0, str0) ∈ ri, ¬ inodekey(m) ∈ ro, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10, fs0[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_core_index_remove#(dentrykey(m, str), fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar; ri); aubifs_core_index_store#(dentrykey(m0, str0), adr2, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar; ri); aubifs_core_index_store#(inodekey(m0), adr4, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar; ri); new_dent := mkdentry(str0, mkdentry(str, m3).ino); old_dent := negdentry(str); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m2, n0, m1).meta, inodenode(inodekey(m), md, true, m2, n0, m1).directory, inodenode(inodekey(m), md, true, m2, n0, m1).nlink, inodenode(inodekey(m), md, true, m2, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, m2, n0, m1).size); new_parent_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).meta, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).directory, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).nlink, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).nsubdirs, inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1).size)⟫ ( ubifs-cons(fs, ri, ro, fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)% ⊦ mkdentry(str, m).ino = m; (s)