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Proof step 42 from proof inv-read (previous step)

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

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 43:
⊦ of-cons(of0, dirs0, files0) → (of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1))

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));% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ dom of[fd, file] = dom of ++ fd; (s)% ⊦ fd ∈ of → dom of ++ fd = dom of; (s)% ⊦ mkfile(m, mode, m0).pos = m0; (s)% ⊦ mkfile(m, mode, m0).pos:= m2 = mkfile(m, mode, m2); (s)% ⊦ of[fd] = file ∧ fd ∈ of → of[fd, file] = of; (s)