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Proof step 15 from proof eq-pos (previous step)

i0 ^ i2 * i0 = i0 ^ i * i0, 2 ≤ i0, ~2 < i2, ~1 ≤ i2, 0 ≤ i2, 1 < i0, ~2 < i, 0 ≤ i, ~1 ≤ i, ∀ i1, i0, j. i→n(i1) < i→n(i2 +1) → i0 ^ i1 = i0 ^ j ∧ 2 ≤ i0 ∧ 0 ≤ j ∧ 0 ≤ i1 ∧ 1 < i0 → i1 = j ⊦ i0 ^ i2 = i0 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: eq-nonzero-01 seq: ⊦ i ≠ 0 → (j * i = j0 * i ↔ j = j0) subst: [j0, i, j] → [i0 ^ i, i0, i0 ^ i2] flags: rewrite

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0 ^ i, i0, i0 ^ i2