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Proof step 30 from proof inv-link (previous step)

fs0[ri[dentrykey(ino, str)]].ino = fs0[ri[dentrykey(ino0, str)]].ino, fs = fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri[inodekey(m3)]].nlink, fs0[ri[inodekey(m3)]].nsubdirs, fs0[ri[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri[dentrykey(ino0, str)]].ino), md, false, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], m = fs0[ri[dentrykey(ino0, str)]].ino, m0 = fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink, m1 = fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, m4 = fs0[ri[inodekey(m3)]].nlink, m5 = fs0[ri[inodekey(m3)]].nsubdirs, m6 = fs0[ri[inodekey(m3)]].size, fs0[ri[dentrykey(ino0, str)]].ino ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m3 ≠ 0, fs0[ri[dentrykey(ino0, str)]].dentry?, fs0[ri[inodekey(ino0)]].directory, fs0[ri[inodekey(m3)]].directory, fs0[ri[inodekey(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), dentrykey(ino0, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(fs0[ri[dentrykey(ino0, str)]].ino) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs0, inodekey(ino) ∈ ri, dentrykey(ino, str) ∈ ri, inodekey(ino0) ∈ ri, ¬ fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].directory, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ inodekey(ino) ∈ ro, ¬ inodekey(fs0[ri[dentrykey(ino0, str)]].ino) ∈ ro, ¬ dentrykey(m3, str0) ∈ ri, ¬ inodekey(m3) ∈ ro, ¬ inodekey(ino0) ∈ ro, fs0[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ ⟪aubifs_core_index_store#(inodekey(m3), adr1, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_store#(dentrykey(m3, str0), adr2, 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); new_dent := mkdentry(str0, m); p_inode0 := mkinode (m3, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).meta, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).directory, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).nlink, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).nsubdirs, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).size); c_inode0 := mkinode (m, inodenode(inodekey(m), md, false, m0 + 1, m1, m2).meta, inodenode(inodekey(m), md, false, m0 + 1, m1, m2).directory, inodenode(inodekey(m), md, false, m0 + 1, m1, m2).nlink, inodenode(inodekey(m), md, false, m0 + 1, m1, m2).nsubdirs, inodenode(inodekey(m), md, false, m0 + 1, 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 31:
fs0[ri[dentrykey(ino, str)]].ino = fs0[ri[dentrykey(ino0, str)]].ino, adr = adr1, fs = fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri[inodekey(m3)]].nlink, fs0[ri[inodekey(m3)]].nsubdirs, fs0[ri[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri[dentrykey(ino0, str)]].ino), md, false, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], key = inodekey(m3), log = ((log0 + adr1 ') + adr2 ') + adr3 ', m = fs0[ri[dentrykey(ino0, str)]].ino, m0 = fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink, m1 = fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, m4 = fs0[ri[inodekey(m3)]].nlink, m5 = fs0[ri[inodekey(m3)]].nsubdirs, m6 = fs0[ri[inodekey(m3)]].size, fs0[ri[dentrykey(ino0, str)]].dentry?, fs0[ri[inodekey(ino)]].directory, fs0[ri[inodekey(m3)]].directory, fs0[ri[inodekey(ino0)]].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(ino0) ∈ ri, dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri[dentrykey(ino0, str)]].ino) ∈ ri, inodekey(m3) ∈ ri, dentrykey(ino0, str) ∈ ri, fs0[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; aubifs_core_index_store#(dentrykey(m3, str0), adr2, 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); new_dent := mkdentry(str0, m); p_inode0 := mkinode (m3, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).meta, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).directory, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).nlink, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).nsubdirs, inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1).size); c_inode0 := mkinode (m, inodenode(inodekey(m), md, false, m0 + 1, m1, m2).meta, inodenode(inodekey(m), md, false, m0 + 1, m1, m2).directory, inodenode(inodekey(m), md, false, m0 + 1, m1, m2).nlink, inodenode(inodekey(m), md, false, m0 + 1, m1, m2).nsubdirs, inodenode(inodekey(m), md, false, m0 + 1, 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(ino0, str)]].ino = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(ino) ∈ ro, inodekey(fs0[ri[dentrykey(ino0, str)]].ino) ∈ ro, dentrykey(m3, str0) ∈ ri, inodekey(m3) ∈ ro, inodekey(ino0) ∈ 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 };