Theorems · Theorem · commutative algebra
ValuativeRel.pow_vle_pow
∀ {R : Type u_2} [inst : Ring R] [inst_1 : ValuativeRel R] {a b : R}, a ≤ᵥ b → ∀ (n : ℕ), a ^ n ≤ᵥ b ^ n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- RingValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- pow_zeroproof · cited by 1,094
- pow_succproof · cited by 374
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.vlestatement and proof · cited by 84
- ValuativeRel.mul_vle_mulproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ValuativeRel.pow_vle_pow_of_one_vleproof · cited by 0
- ValuativeRel.pow_vle_pow_of_vle_oneproof · cited by 0