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Proof step 2 from proof coef-divides-rec-lower (previous step)

j ≤ i, 0 < j, 0 < i ⊦ j | binom_coef(i, j - 1) * (i + 1 - j)

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: coef-mult-rec-lower seq: ⊦ 0 < j ∧ j ≤ i → binom_coef(i, j) * j = binom_coef(i, j - 1) * (i + 1 - j) subst: [j, i] → [j, i] flags: current, []

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i