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Proof step 4 from proof mk-inj (previous step)

b ' + mklist(b, m0) = mklist(b, n), ∀ a, b, n. mklist(a, m0) = mklist(b, n) → m0 = 0 ∨ a = b ∧ m0 = n ⊦ n = 0, m0 + 1 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-last inst: name: mk-rec seq: ⊦ m ≠ 0 → mklist(a, m) = a + mklist(a, m - 1) subst: [m, a] → [n, b] flags: rewrite, current

Additional information

Used simplifier rules: mk-inj-01: ⊦ mklist(a, m) = mklist(a, n) ↔ m = n;%c: ⊦ a + x = a ' + x; from specification list%app-01: ⊦ x + y = x + z ↔ y = z; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%eq-02: n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2 Used terms: n, b