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Proof step 13 from proof fac-le (previous step)

0 ≤ i1, 0 ≤ i2, ∀ i0, j. i→n(i0) < i→n(i1 + 1) → 0 < i0 ∧ 0 < j → (fac(i0) ≤ fac(j) ↔ i0 ≤ j) ⊦ 0 < i1 ∧ 0 < i2, (i1 + 1) * fac(i1) ≤ (i2 + 1) * fac(i2) ↔ i1 ≤ i2

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 0 < i1

Additional information

Used simplifier rules: fac-zero: ⊦ i ≤ 0 → fac(i) = 1;%fac-le-zero: ⊦ i * fac(j) ≤ 0 ↔ i ≤ 0;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%irreflexivity: ⊦ ¬ i < i; from specification oelem[intlista]%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs%mone-05: ⊦ i ≤ ~1 ↔ i < 0; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used formulas: 0 < i1