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Theorems · Theorem · order theory

abs_le_of_sq_le_sq

∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a b : α},
  a ^ 2 ≤ b ^ 2 → 0 ≤ b → |a| ≤ b
Defined in
Mathlib.Algebra.Order.Ring.Abs
Cited by
2 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingLinearOrderIsStrictOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

le_of_sq_le_sq · cited by 8le_of_sq_le_sqabs_le_of_sq_le_sq' · cited by 3abs_le_of_sq_le_sq'LinearOrder · cited by 8572LinearOrderRing · cited by 7463RingIsStrictOrderedRing · cited by 2490IsStrictOrderedRingabs · cited by 1814absabs_of_nonneg · cited by 279abs_of_nonnegsq_le_sq · cited by 16sq_le_sqabs_le_of_sq_le_sqCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.