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Proof step 32 from proof refine-evict (previous step)

fs[ri1[inodekey(m)]].nlink = 0, dirs = abs-dirs(fs, ri1), files = abs-files(fs, ri1), m ≠ ROOT_INO, orphans(fs, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri1), abs-files(fs, ri1)), file-node-cons(fs, ri1), log-cons(log, fs), orphans-cons(fs, ri1, orphans(fs, ri1)), replay-cons-strong(fs, ri1, orphans(fs, ri1), fi, fo, log), ri-inj(ri1), ri-inj(fi), ubifs-cons(fs, ri1, orphans(fs, ri1), fi, fo, log), inodekey(m) ∈ ri1, asynced → boolvar1, ∀ ino. inodekey(ino) ∈ ri1 ∧ fs[ri1[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO → links(ino, fs, ri1) = ∅, ∀ ino. inodekey(ino) ∈ ri1 ∧ fs[ri1[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO → dentrykeys(inodekey(ino), ri1) = ∅, fs[ri1[inodekey(m)]].directory ∧ m0 = 0 ∧ m2 = fs[ri1[inodekey(m)]].size ∧ m1 = fs[ri1[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri1[inodekey(m)]].directory ∧ m0 = 0 ∧ m1 = 0 ∧ ¬ boolvar2 ⊦ ⟨afs_evict#(mkinode(m, md, boolvar2, m0, m1, m2), asynced; err0, dirs, files)⟩ ( dirs = abs-dirs(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ∧ files = abs-files(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ∧ orphans(abs-dirs(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)), abs-files(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m))) = abs-keys(orphans(fs, ri1)) -- m ∧ (asynced → boolvar1) ∧ ESUCCESS = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 33:
afs-cons(dirs, files), pre-evict(inode, dirs, files) ⊦ ⟪afs_evict#(inode, asynced; err, dirs, files)⟫ afs-cons(dirs, files)
Proof step 34:
fs[ri1[inodekey(m)]].nlink = 0, asynced0 ↔ asynced, dirs = abs-dirs(fs, ri1), files = abs-files(fs, ri1), inode0 = mkinode(m, md, boolvar2, m0, m1, m2), fo.inodes?, orphans(fs, ri1).inodes?, afs-cons(abs-dirs(fs, ri1), abs-files(fs, ri1)), afs-cons(dirs, files), file-node-cons(fs, ri1), log-cons(log, fs), orphans-cons(fs, ri1, orphans(fs, ri1)), pre-evict(mkinode(m, md, boolvar2, m0, m1, m2), dirs, files), replay-cons-strong(fs, ri1, orphans(fs, ri1), fi, fo, log), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs, ri1, orphans(fs, ri1), fi, fo, log), inodekey(m) ∈ ri1, asynced → boolvar1, ∀ ino. inodekey(ino) ∈ ri1 ∧ fs[ri1[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO → dentrykeys(inodekey(ino), ri1) = ∅, ∀ ino. inodekey(ino) ∈ ri1 ∧ fs[ri1[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO → links(ino, fs, ri1) = ∅, fs[ri1[inodekey(m)]].directory ∧ m0 = 0 ∧ m2 = fs[ri1[inodekey(m)]].size ∧ m1 = fs[ri1[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri1[inodekey(m)]].directory ∧ m0 = 0 ∧ m1 = 0 ∧ ¬ boolvar2 ⊦ [afs_evict#(mkinode(m, md, boolvar2, m0, m1, m2), asynced; err0, dirs, files)] ( afs-cons(dirs, files) → dirs = abs-dirs(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ∧ files = abs-files(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ∧ orphans(abs-dirs(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)), abs-files(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m))) = abs-keys(orphans(fs, ri1)) -- m ∧ (asynced → boolvar1) ∧ ESUCCESS = err0), m = ROOT_INO

Rule argument

spec: afs-asm name: inv-evict seq: afs-cons(dirs, files), pre-evict(inode, dirs, files) ⊦ ⟪afs_evict#(inode, asynced; err, dirs, files)⟫ afs-cons(dirs, files) subst: [asynced, inode, files, dirs, err] → [asynced, mkinode(m, md, boolvar2, m0, m1, m2), files, dirs, err0] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ pre-evict(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files) ∧ inode.ino ≠ ROOT_INO; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)