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

j ≤ i, 0 < j, 0 < i ⊦ binom_coef(i, j) = (binom_coef(i, j - 1) * (i + 1 - j)) / 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: coef-zero: ⊦ 0 ≤ i → binom_coef(i, 0) = 1;%coef-neg: ⊦ j < 0 → binom_coef(i, j) = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%numsub: ⊦ (* i) + i0 - (* j) = (i - j) + i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div Used terms: j, i