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Proof step 16 from proof refine-mkdir (previous step)

p_inode0.nlink = fs[ri[inodekey(p_inode0.ino)]].nlink, p_inode0.nsubdirs = fs[ri[inodekey(p_inode0.ino)]].nsubdirs, p_inode0.size = fs[ri[inodekey(p_inode0.ino)]].size, c_inode = p_inode1, dent = old_dent, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), p_inode = p_inode0, ro = orphans(fs, ri), p_inode0.directory, fs[ri[inodekey(p_inode0.ino)]].directory, orphans(fs, ri).inodes?, fo.inodes?, old_dent.negdentry?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(p_inode0.ino) ∈ ri, ¬ dentrykey(p_inode0.ino, old_dent.name) ∈ ri, asynced → boolvar, links(p_inode0.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode0.ino = ROOT_INO, p_inode0.nlink ≠ 0 ∨ p_inode0.ino = ROOT_INO ⊦ [aubifs_mkdir#(md, fi, orphans(fs, ri), fo; p_inode, c_inode, dent, err, ri, fs, log, boolvar)] ( 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) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨afs_mkdir#(md; p_inode0, p_inode1, old_dent, 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(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), p_inode0.nlink = 0 ∧ p_inode0.ino ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
p_inode0.nlink = fs[ri[inodekey(p_inode0.ino)]].nlink, p_inode0.nsubdirs = fs[ri[inodekey(p_inode0.ino)]].nsubdirs, p_inode0.size = fs[ri[inodekey(p_inode0.ino)]].size, c_inode = p_inode1, dent = old_dent, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), old_dent = negdentry(str), p_inode = p_inode0, ro = orphans(fs, ri), fs[ri[inodekey(p_inode0.ino)]].directory, p_inode0.directory, fo.inodes?, orphans(fs, ri).inodes?, old_dent.negdentry?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(p_inode0.ino) ∈ ri, asynced → boolvar, p_inode0.nlink ≠ 0 ∨ p_inode0.ino = ROOT_INO, links(p_inode0.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode0.ino = ROOT_INO ⊦ [aubifs_mkdir#(md, fi, orphans(fs, ri), fo; p_inode, c_inode, dent, err, ri, fs, log, boolvar)] ( 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) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨afs_mkdir#(md; p_inode0, p_inode1, old_dent, 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(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), dentrykey(p_inode0.ino, str) ∈ ri, p_inode0.nlink = 0 ∧ p_inode0.ino ≠ ROOT_INO

Rule argument

spec: dentry name: elim-02 seq: ⊦ dent.negdentry? → (str = dent.name ↔ dent = negdentry(str)) subst: [dent, str] → [old_dent, str]

Additional information

Used simplifier rules: ⊦ dent.negdentry? → (str = dent.name ↔ dent = negdentry(str)); (elim) Used terms: old_dent, str