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

j ≤ i, 0 < j, 0 < i ⊦ binom_coef(i, j) = (binom_coef(i - 1, j - 1) * i) / j

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ j ≤ i → i * binom_coef(i - 1, j - 1) = j * binom_coef(i, j)

Rule argument

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

Additional information

Used simplifier rules: coef-neg: ⊦ j < 0 → binom_coef(i, j) = 0;%coef-zero: ⊦ 0 ≤ i → binom_coef(i, 0) = 1;%commutativity: ⊦ i * j = j * i; from specification int-mult%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div Used terms: j, i