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Proof step 35 from proof inv-read (previous step)

files[m] = mkfile(m1, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), dom of < ino2, afs-cons(dirs, files), of-cons(of, dirs, files), m ∈ files, fd ∈ of, m0 ≤ m1, n ≤ # buf ⊦ ino = 0, mode ≠ MODE_R ∧ mode ≠ MODE_RW, of-cons(of[fd, of[fd].pos:= (of[fd].pos + ino)], dirs, files) ∧ dom of[fd, of[fd].pos:= (of[fd].pos + ino)] < ino2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
⊦ 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 37:
files[m] = mkfile(m1, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), dom of < ino2, afs-cons(dirs, files), of-cons(of, dirs, files), m ∈ files, fd ∈ of, n0 ∈ of[fd, mkfile(m, mode, m0 + ino)], n0 ∈ of, of[n0].ino ∈ files, m0 ≤ m1, n ≤ # buf ⊦ ino = 0, of[fd, mkfile(m, mode, m0 + ino)][n0].ino ∈ files, mode ≠ MODE_R ∧ mode ≠ MODE_RW

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));%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkfile(m, mode, m0).ino = m; (s)% ⊦ fd = fd0 → of[fd0, file][fd] = file; (s)% ⊦ fd ∈ of[fd0, file] ↔ fd = fd0 ∨ fd ∈ of; (ws)% ⊦ mkfile(m, mode, m0).pos:= m2 = mkfile(m, mode, m2); (s)% ⊦ mkfile(m, mode, m0).pos = m0; (s)% ⊦ fd ∈ of → dom of ++ fd = dom of; (s)% ⊦ dom of[fd, file] = dom of ++ fd; (s)