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Proof step 63 from proof all_prime_divisors-div (previous step)

all_prime_divisors(i0 / i) = i0 ' -1l i, prime(i0), 0 < i * i0, 0 ≤ i * i0, i < i * i0, prime(i), 2 ≤ i * i0, i | i0, ∀ j0. i < j0 ∧ j0 < i * i0 ∧ prime(j0) → ¬ j0 | i * i0, ∀ j0, i1. i→n(j0) < i→n(i * i0) → i1 | j0 ∧ prime(i1) ∧ 0 < j0 → all_prime_divisors(j0 / i1) = all_prime_divisors(j0) -1l i1 ⊦ i0 ' = (i0 ' -1l i) + i ', prime(i * i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del inst: intlista name: one-01-01 seq: ⊦ i ≠ i0 → i ' -1l i0 = i ' subst: [i0, i] → [i, i0] flags: rewrite

Additional information

Used simplifier rules: one-01: ⊦ i ' -1l i = []; from specification list-del[intlista]%Nil: ⊦ [] + ints = ints; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%c-04: ⊦ i ' = i0 ' ↔ i = i0; from specification list[intlista] Used terms: i, i0