Theorems · Theorem · order theory
Int.cast_le_neg_one_of_neg
∀ {R : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : ℤ}, a < 0 → ↑a ≤ -1- Defined in
- Mathlib.Algebra.Order.Ring.Cast
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Int.cast_oneproof · cited by 371
- Int.cast_negproof · cited by 224
- Int.cast_leproof · cited by 28
Cited by2
Results whose statement or proof uses this declaration.
- Int.nneg_mul_add_sq_of_abs_le_oneproof · cited by 1
- Int.cast_le_neg_one_or_one_le_cast_of_ne_zeroproof · cited by 1