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Proof step 69 from proof refine-mkdir (previous step)

fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), adr = adr1, dirs = abs-dirs(fs1, ri1), files = abs-files(fs1, ri1), fs = fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], key = inodekey(m0), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri1[key, adr], ri0 = ri1, ro = orphans(fs1, ri1), ro0 = orphans(fs1, ri1), fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, orphans(fs1, ri1)), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri1[inodekey(m0)] ∈ fs1, inodekey(m0) ∈ ri1, asynced → boolvar0, m1 ≠ 0 ∨ m0 = ROOT_INO, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO ⊦ [aubifs_core_index_store# (dentrykey(m0, str), adr2, fi, orphans(fs1, ri0), fo, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); aubifs_core_index_store# (inodekey(n), adr3, fi, orphans(fs1, ri0), fo, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); dent := mkdentry(str, n); p_inode := mkinode (m0, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).meta, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).directory, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).nlink, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).nsubdirs, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).size); c_inode := mkinode (n, inodenode(inodekey(n), md, true, 1, 0, 0).meta, inodenode(inodekey(n), md, true, 1, 0, 0).directory, inodenode(inodekey(n), md, true, 1, 0, 0).nlink, inodenode(inodekey(n), md, true, 1, 0, 0).nsubdirs, inodenode(inodekey(n), md, true, 1, 0, 0).size)] ( ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, ro0, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, ro0, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, ro0) ∧ ri-inj(ri) ∧ log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]) ∧ m0 ≠ 0 → ⟨old_dent := negdentry(str); p_inode0 := mkinode (m0, md2, true, inodenode(key0, md1, true, m1, m2, m6).nlink, inodenode(key0, md1, true, m1, m2, m6).nsubdirs, inodenode(key0, md1, true, m1, m2, m6).size); afs_mkdir#(md; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ files = abs-files (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ orphans (abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri), abs-files (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ ESUCCESS = err0)), adr1 = adr3, adr1 = adr2, adr2 = adr3, n = 0, dentrykey(m0, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, m1 = 0 ∧ m0 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), ri = ri1[inodekey(m0), adr1], adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, n ≠ 0, orphans(fs1, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, orphans(fs1, ri1)), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri-inj(ri1), ri-inj(fi), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), inodekey(m0) ∈ ri1, ri1[inodekey(m0)] ∈ fs1, ¬ adr3 ∈ fs1, ¬ adr2 ∈ fs1, ¬ adr1 ∈ fs1, ¬ inodekey(n) ∈ ri1, ¬ inodekey(n) ∈ fo, ¬ dentrykey(m0, str) ∈ ri1, asynced → boolvar0, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO, m1 ≠ 0 ∨ m0 = ROOT_INO ⊦ [aubifs_core_index_store# (dentrykey(m0, str), adr2, fi, orphans(fs1, ri1), fo, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); aubifs_core_index_store# (inodekey(n), adr3, fi, orphans(fs1, ri1), fo, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); dent := mkdentry(str, n); p_inode := mkinode (m0, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).meta, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).directory, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).nlink, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).nsubdirs, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).size); c_inode := mkinode (n, inodenode(inodekey(n), md, true, 1, 0, 0).meta, inodenode(inodekey(n), md, true, 1, 0, 0).directory, inodenode(inodekey(n), md, true, 1, 0, 0).nlink, inodenode(inodekey(n), md, true, 1, 0, 0).nsubdirs, inodenode(inodekey(n), md, true, 1, 0, 0).size)] ( ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, orphans(fs1, ri1)) ∧ ri-inj(ri) ∧ log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]) ∧ m0 ≠ 0 → ⟨old_dent := negdentry(str); p_inode0 := mkinode (m0, md2, true, inodenode(key0, md1, true, m1, m2, m6).nlink, inodenode(key0, md1, true, m1, m2, m6).nsubdirs, inodenode(key0, md1, true, m1, m2, m6).size); files := abs-files(fs1, ri1); dirs := abs-dirs(fs1, ri1); afs_mkdir#(md; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ files = abs-files (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ orphans (abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri), abs-files (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri)) = abs-keys(orphans(fs1, ri1)) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ ESUCCESS = err0)), m1 = 0 ∧ m0 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)