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Proof step 5 from proof coef-succ (previous step)

0 ≤ j ⊦ fac(j + 1) / fac(j) = j + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-fac inst: name: fac-rec seq: ⊦ 0 < i → fac(i) = i * fac(i - 1) subst: [i] → [j + 1] flags: rewrite, current

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0;%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%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: j + 1