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Proof step 52 from proof inv-seek (previous step)

err = ESUCCESS, dom of < ino, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ whence = SEEK_END, whence = SEEK_CUR, of-cons(of[fd, of[fd].pos:= n], dirs, files) ∧ dom of[fd, of[fd].pos:= n] < ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
⊦ of-cons(of0, dirs0, files0) → (of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1))
Proof step 54:
dom of < ino, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, n0 ∈ of[fd, of[fd].pos:= n], n0 ∈ of → of[n0].ino ∈ files ⊦ whence = SEEK_CUR, whence = SEEK_END, of[fd, of[fd].pos:= n][n0].ino ∈ files

Rule argument

Additional information

Used simplifier rules: of-cons-reduce: ⊦ of-cons(of0, dirs0, files0) → ( of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1));% ⊦ fd ∈ of → dom of ++ fd = dom of; (s)% ⊦ dom of[fd, file] = dom of ++ fd; (s)