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Proof step 11 from proof of-cons-reduce (previous step)

of0[n] = mkfile(m, mode, m0), n ∈ of1, n ∈ of0 → m ∈ files0, ∀ n. n ∈ of0 → of0[n].ino ∈ files0, ∀ n. n ∈ of1 → of1[n].ino ∈ files1 ⊦ of1[n].ino ∈ files1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
of0[n] = mkfile(m, mode, m0), of1[n] = mkfile(m1, mode0, m2), n ∈ of1, n ∈ of0 → m ∈ files0, ∀ n. n ∈ of1 → of1[n].ino ∈ files1, ∀ n. n ∈ of0 → of0[n].ino ∈ files0 ⊦ m1 ∈ files1

Rule argument

spec: file name: elim seq: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0) subst: [file, m, mode, m0] → [of1[n], m1, mode0, m2]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of1[n], m1, mode0, m2