Theorems · Theorem · real analysis
Real.le_rpow_add
∀ {x : ℝ}, 0 ≤ x → ∀ (y z : ℝ), x ^ y * x ^ z ≤ x ^ (y + z)For 0 ≤ x, the only problematic case in the equality x ^ y * x ^ z = x ^ (y + z) is for
x = 0 and y + z = 0, where the right-hand side is 1 while the left-hand side can vanish.
The inequality is always true, though, and given in this lemma.
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- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
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