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Proof step 4 from proof mod-pot-pot (previous step)

0 < j, 0 ≤ i0, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 ≤ i1 ∧ 0 < j → (i |%| j) ^ i1 |%| j = i ^ i1 |%| j ⊦ (i |%| j) ^ i0 |%| j = i ^ i0 |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 6:
0 < i0, 0 < j, 0 ≤ i0, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 ≤ i1 ∧ 0 < j → (i |%| j) ^ i1 |%| j = i ^ i1 |%| j ⊦ (i |%| j) ^ i0 |%| j = (i ^ i0 -1 * i) |%| j

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i0, i] flags: rewrite

Additional information

Used simplifier rules: 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]%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot Used terms: i0, i