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Proof step 2 from proof refine-fsyncdir (previous step)

dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), orphans(dirs, files) = abs-keys(ro), fo.inodes?, ro.inodes?, afs-cons(dirs, files), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), asynced → boolvar ⊦ ⟪aubifs_fsyncdir#(inode, boolvar0; ; err)⟫ ⟨afs_fsyncdir#(inode, boolvar0, dirs, files, asynced; ; err0)⟩ ((dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (asynced → boolvar)) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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 ⊦ ⟪aubifs_fsyncdir#(inode, boolvar0; ; err)⟫ ⟨afs_fsyncdir#(inode, boolvar0, abs-dirs(fs, ri), abs-files(fs, ri), asynced; ; err0)⟩ ((asynced → boolvar) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ro.inodes? → (abs-keys(ro) = abs-keys(orphans(fs, ri)) ↔ ro = orphans(fs, ri)); (s)%⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)