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Proof step 4 from proof coef-succ (previous step)

0 ≤ j ∧ j ≤ j + 1, 0 ≤ j ⊦ fac(j + 1) / (fac(j + 1 - j) * fac(j)) = j + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 ≤ j ⊦ fac(j + 1) / fac(j) = j + 1

Rule argument

Additional information

Used simplifier rules: fac-one: ⊦ fac(1) = 1;%lep: ⊦ i ≤ i + j ↔ 0 ≤ j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-add: ⊦ i + j - i = j; from specification int-abs