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Proof step 1 from proof coef-rec-add-02 (conclusion)

⊦ 0 < j ∧ j ≤ i + 1 → binom_coef(i + 1, j) = binom_coef(i, j - 1) + binom_coef(i, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-fac inst: name: coef-rec-add-01 seq: ⊦ 0 < j ∧ j ≤ i → binom_coef(i, j) = binom_coef(i - 1, j - 1) + binom_coef(i - 1, j) subst: [j, i] → [j, i + 1] flags: rewrite, current

Additional information

Used simplifier rules: numsub: ⊦ (* i) + i0 - (* j) = (i - j) + i0; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2 Used terms: j, i + 1