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Proof step 3 from proof recovery (previous step)

dirs0 = abs-dirs(fs0, ri), files0 = abs-files(fs0, ri), fo0.inodes?, orphans(fs0, ri).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), fi0, fo0, log0), ri-inj(fi0), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi0, fo0, log0) ⊦ ⟪aubifs_replay#(boolvar2; ri0, fi0, ro0, fo0, fs0, log0, boolvar3; err)⟫ ( ( err = ESUCCESS → ⟨dirs := dirs0 \ orphans(dirs0, files0), files := files0 \ orphans(dirs0, files0); afs_recovery#(boolvar2; dirs, files; asynced, err0)⟩ ( dirs = abs-dirs(fs0, ri0) ∧ files = abs-files(fs0, ri0) ∧ orphans(abs-dirs(fs0, ri0), abs-files(fs0, ri0)) = abs-keys(ro0) ∧ (asynced → boolvar3) ∧ ESUCCESS = err0)) ∧ ( err ≠ ESUCCESS → (∀ dirs, files, boolvar. ⟨afs_recovery#(boolvar2; dirs1, files1; asynced0, err0)⟩ (dirs = dirs1 ∧ files = files1 ∧ (boolvar ↔ asynced0) ∧ err = err0))))

User applied rule insert program lemma

And obtained the following new goals

Proof step 4:
replay-safe(log, fs, fi ⊖ fo), fo.inodes?, fs0 = fs, fi0 = fi, fo0 = fo, log0 = log ⊦ ⟪aubifs_replay#(boolvar0; ri, fi, ro, fo, fs, log, boolvar; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ri = replay(log, fs, fi, fo) ∧ ro = ∅ ∧ fs = fs0 ∧ fi = fi0 ∧ fo = fo0 ∧ log = log0 ∧ boolvar))
Proof step 5:
boolvar1 ↔ boolvar2, dirs0 = abs-dirs(fs0, ri), fi0 = fi0, fi1 = fi0, files0 = abs-files(fs0, ri), fo0 = fo0, fo1 = fo0, fs0 = fs0, fs1 = fs0, log0 = log0, log1 = log0, orphans(fs0, ri).inodes?, fo0.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), fi0, fo0, log0), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-inj(ri), ri-inj(fi0), ubifs-cons(fs0, ri, orphans(fs0, ri), fi0, fo0, log0) ⊦ [aubifs_replay#(boolvar2; ri0, fi0, ro0, fo0, fs0, log0, boolvar3; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ri0 = replay(log0, fs0, fi0, fo0) ∧ ro0 = ∅ ∧ fs0 = fs1 ∧ fi0 = fi1 ∧ fo0 = fo1 ∧ log0 = log1 ∧ boolvar3) → ( err = ESUCCESS → ⟨dirs := dirs0 \ orphans(dirs0, files0), files := files0 \ orphans(dirs0, files0); afs_recovery#(boolvar2; dirs, files; asynced, err0)⟩ ( dirs = abs-dirs(fs0, ri0) ∧ files = abs-files(fs0, ri0) ∧ orphans(abs-dirs(fs0, ri0), abs-files(fs0, ri0)) = abs-keys(ro0) ∧ (asynced → boolvar3) ∧ ESUCCESS = err0)) ∧ ( err ≠ ESUCCESS → (∀ dirs, files, boolvar. ⟨afs_recovery#(boolvar2; dirs1, files1; asynced0, err0)⟩ (dirs = dirs1 ∧ files = files1 ∧ (boolvar ↔ asynced0) ∧ err = err0))))

Rule argument

spec: aubifs-asm name: replay-prog seq: replay-safe(log, fs, fi ⊖ fo), fo.inodes?, fs0 = fs, fi0 = fi, fo0 = fo, log0 = log ⊦ ⟪aubifs_replay# (boolvar0; ri, fi, ro, fo, fs, log, boolvar; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → ri = replay(log, fs, fi, fo) ∧ ro = ∅ ∧ fs = fs0 ∧ fi = fi0 ∧ fo = fo0 ∧ log = log0 ∧ boolvar)) subst: [boolvar0, boolvar, log, fs, fo, ro, fi, ri, err, fs0, fi0, fo0, log0] → [boolvar2, boolvar3, log0, fs0, fo0, ro0, fi0, ri0, err, fs0, fi0, fo0, log0] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) → replay-safe(log, fs, fi ⊖ fo); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → fo.inodes?; (ss)