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Proof step 4 from proof coef-pred-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 < j ⊦ fac(j) / fac(j - 1) = j

Rule argument

Additional information

Used simplifier rules: fac-one: ⊦ fac(1) = 1;%lep: ⊦ i ≤ i + j ↔ 0 ≤ j; from specification int-abs%sub-le: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ 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%sub-sub-04: ⊦ i - (j - j0) = i + j0 - j; from specification int-abs