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Proof step 19 from proof refine-write-inode (previous step)

dirs = abs-dirs(fs0, ri), err = ESUCCESS, files = abs-files(fs0, ri), fs = fs0[adr1, nd], log = log0 + adr1, nd = inodenode(inodekey(m), md, boolvar0, m0, m1, m2), ro = orphans(fs0, ri), ro0 = orphans(fs0, ri), fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ', fs0), node-cons(nd.key, nd), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), asynced → boolvar1, fs0[(∅)[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO → inodekey(m) ∈ ri, inodekey(m) ∈ ri ∧ fs0[ri[inodekey(m)]].directory ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m2 = fs0[ri[inodekey(m)]].size ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ inodekey(m) ∈ ri ∧ ¬ fs0[ri[inodekey(m)]].directory ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar0, inodekey(m) ∈ ri ∧ ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∨ inodekey(m) ∈ ri ∧ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri[inodekey(m)]].size ⊦ ⟪aubifs_core_index_store#(inodekey(m), adr1, fi, ro0, fo, fs, log, boolvar; ri)⟫ ⟨afs_write_inode#(mkinode(m, md, boolvar0, m0, m1, m2); err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ err = err0), dups(adr1 ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), ro = orphans(fs0, ri), m ≠ 0, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), ¬ adr1 ∈ fs0, fs0[(∅)[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO → inodekey(m) ∈ ri, asynced → boolvar1, inodekey(m) ∈ ri ∧ ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∨ inodekey(m) ∈ ri ∧ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri[inodekey(m)]].size, inodekey(m) ∈ ri ∧ fs0[ri[inodekey(m)]].directory ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m2 = fs0[ri[inodekey(m)]].size ∧ m1 = fs0[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ inodekey(m) ∈ ri ∧ ¬ fs0[ri[inodekey(m)]].directory ∧ m0 = fs0[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar0 ⊦ ⟪aubifs_core_index_store# (inodekey(m), adr1, fi, orphans(fs0, ri), fo, fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], log0 + adr1 ', boolvar; ri)⟫ ⟨afs_write_inode#(mkinode(m, md, boolvar0, m0, m1, m2); err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri) ∧ files = abs-files(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri) ∧ orphans (abs-dirs(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri), abs-files(fs0[adr1, inodenode(inodekey(m), md, boolvar0, m0, m1, m2)], ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ax + adr = ax + adr '; (s)% ⊦ ¬ dups(adr '); (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)