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Proof step 3 from proof refine-write-inode (previous step)

dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), ro = orphans(fs, ri), fo.inodes?, orphans(fs, ri).inodes?, 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), asynced → boolvar, inodekey(inode.ino) ∈ ri ∧ fs[ri[inodekey(inode.ino)]].directory ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.size = fs[ri[inodekey(inode.ino)]].size ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs ∧ inode.directory ∨ inodekey(inode.ino) ∈ ri ∧ ¬ fs[ri[inodekey(inode.ino)]].directory ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory ⊦ ⟪aubifs_write_inode#(inode, fi, orphans(fs, ri), fo; err, ri, fs, log, boolvar)⟫ ⟨afs_write_inode#(inode; 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) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), inode = mkinode(m, md, boolvar0, m0, m1, m2), ro = orphans(fs, ri), orphans(fs, ri).inodes?, fo.inodes?, 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), asynced → boolvar, inodekey(m) ∈ ri ∧ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ inodekey(m) ∈ ri ∧ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar0 ⊦ ⟪aubifs_write_inode#(inode, fi, orphans(fs, ri), fo; err, ri, fs, log, boolvar)⟫ ⟨afs_write_inode#(inode; 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) ∧ err = err0)

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] → [inode, m, md, boolvar0, m0, m1, m2]

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: inode, m, md, boolvar0, m0, m1, m2