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Proof step 110 from proof refine-seek (previous step)

err0 = ESUCCESS, fh = ofh[fd], n = n0, ofh = abs-of(of), root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), fd ∈ of, fd ∈ ofh, psynced → asynced ⊦ whence = SEEK_END, whence = SEEK_CUR, fh.fid ∈ abs-files(files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 111:
root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), fd ∈ of, psynced → asynced ⊦ whence = SEEK_CUR, whence = SEEK_END, of[fd].ino ∈ files

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files; (s)% ⊦ mkfh(fid, mode, m).fid = fid; (s)%fd ∈ of ⊦ abs-of(of)[fd] = mkfh(⌜of[fd].ino⌝ , of[fd].mode, of[fd].pos); (s)% ⊦ fd ∈ abs-of(of) ↔ fd ∈ of; (s)