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Proof step 19 from proof inv-link (previous step)

fs[ri[dentrykey(ino, str)]].ino = fs[ri[dentrykey(ino0, str)]].ino, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, m = fs[ri[dentrykey(ino0, str)]].ino, m0 = fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink, m1 = fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, fs[ri[dentrykey(ino0, str)]].dentry?, fs[ri[inodekey(ino)]].directory, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fs[ri[inodekey(ino0)]].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(ino0) ∈ ri, dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, inodekey(fs[ri[dentrykey(ino0, str)]].ino) ∈ ri, inodekey(p_inode.ino) ∈ ri, dentrykey(ino0, str) ∈ ri, ¬ fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].directory, ¬ inodekey(ino0) ∈ ro, ¬ inodekey(p_inode.ino) ∈ ro, ¬ dentrykey(p_inode.ino, str0) ∈ ri, ¬ inodekey(fs[ri[dentrykey(ino0, str)]].ino) ∈ ro, ¬ inodekey(ino) ∈ ro, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO, fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO ⊦ ⟪aubifs_core_journal_add3# (inodenode(inodekey(p_inode.ino), p_inode.meta, true, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 1), dentrynode(dentrykey(p_inode.ino, str0), m), inodenode(inodekey(m), md, false, m0 + 1, m1, m2), ri, fi, ro, fo ; adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(p_inode.ino), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(p_inode.ino, str0), adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr, fi, ro, fo, fs, log, boolvar; ri); new_dent := mkdentry(str0, m); p_inode0 := mkinode (p_inode.ino, inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 1).meta, inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 1).directory, inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 1).nlink, inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 1).nsubdirs, inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 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, 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

Proof step 20:
fs[ri[dentrykey(ino, str)]].ino = fs[ri[dentrykey(ino0, str)]].ino, boolvar0, m = fs[ri[dentrykey(ino0, str)]].ino, m0 = fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nlink, m1 = fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, m4 = fs[ri[inodekey(m3)]].nlink, m5 = fs[ri[inodekey(m3)]].nsubdirs, m6 = fs[ri[inodekey(m3)]].size, p_inode = mkinode(m3, md0, boolvar0, m4, m5, m6), fs[ri[dentrykey(ino0, str)]].dentry?, fs[ri[inodekey(ino0)]].directory, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(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(ino0, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(fs[ri[dentrykey(ino0, str)]].ino) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, inodekey(ino) ∈ ri, dentrykey(ino, str) ∈ ri, inodekey(ino0) ∈ ri, fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ ⟪aubifs_core_journal_add3# (inodenode(inodekey(m3), md0, true, m4, m5, m6 + 1), dentrynode(dentrykey(m3, str0), m), inodenode(inodekey(m), md, false, m0 + 1, m1, m2), ri, fi, ro, fo ; adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m3), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(m3, str0), adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr, fi, ro, fo, fs, log, boolvar; ri); new_dent := mkdentry(str0, m); p_inode0 := mkinode (m3, inodenode(inodekey(m3), md0, boolvar0, m4, m5, m6 + 1).meta, inodenode(inodekey(m3), md0, boolvar0, m4, m5, m6 + 1).directory, inodenode(inodekey(m3), md0, boolvar0, m4, m5, m6 + 1).nlink, inodenode(inodekey(m3), md0, boolvar0, m4, m5, m6 + 1).nsubdirs, inodenode(inodekey(m3), md0, boolvar0, 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, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), fs[ri[inodekey(fs[ri[dentrykey(ino0, str)]].ino)]].directory, inodekey(ino0) ∈ ro, inodekey(m3) ∈ ro, dentrykey(m3, str0) ∈ ri, inodekey(fs[ri[dentrykey(ino0, str)]].ino) ∈ ro, inodekey(ino) ∈ ro

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [p_inode, m3, md0, boolvar, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: p_inode, m3, md0, boolvar, m4, m5, m6