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Proof step 50 from proof refine-evict (previous step)

fs[ri1[inodekey(m)]].nlink = 0, fs[ri1[inodekey(m)]].directory, orphans(fs, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri1) -- m, abs-files(fs, ri1)), 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, inodekey(ino) ∈ 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) = ∅ ⊦ abs-files(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m))[ino] = mkfile(fs[ri1[inodekey(ino)]].size, fs[ri1[inodekey(ino)]].meta, fs[ri1[inodekey(ino)]].nlink, abs-content(ino, fs, ri1)), m = ROOT_INO, fs[ri1[inodekey(ino)]].directory

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-abs name: at-files seq: ⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri) subst: [ino, ri, fs] → [ino, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m), fs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)%key ≠ key0 ⊦ (ri -- key0)[key] = ri[key]; (s)% ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]); (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ ¬ inodekey(m).data?; (s)%⊦ mkfile(m0, md0, n0, content0) = mkfile(m1, md1, n1, content1) ↔ ¬(n0 ≠ n1 ∨ md0 ≠ md1 ∨ m0 ≠ m1 ∨ content0 ≠ content1); (ss)%⊦ content = abs-content(ino, fs, ri) ↔ (∀ n. (n ∈ content ↔ datakey(ino, n) ∈ ri) ∧ (n ∈ content → content[n] = fs[ri[datakey(ino, n)]].data)); (ss)% ⊦ n ∈ abs-content(ino, fs, ri) ↔ datakey(ino, n) ∈ ri; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)% ⊦ datakey(m, m0).data?; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ inodekey(m).ino = m; (s)%⊦ datakey(ino, n) ∈ ri → abs-content(ino, fs, ri)[n] = fs[ri[datakey(ino, n)]].data; (s) Used terms: ino, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m), fs