Theorems · Theorem · order theory
Subtype.range_val
∀ {α : Type u_1} {s : Set α}, Set.range Subtype.val = sA variant of range_coe. Try to use range_coe if possible.
This version is useful when defining a new type that is defined as the subtype of something.
In that case, the coercion doesn't fire anymore.
- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.rangestatement · cited by 4,705
- Subtype.range_coeproof · cited by 98
Cited by42
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Opens.opensRange_ιproof · cited by 29
- AlgebraicGeometry.Scheme.Opens.range_ιproof · cited by 16
- AlgebraicGeometry.isAffineOpen_opensRangeproof · cited by 13
- IntermediateField.fieldRange_valproof · cited by 9
- Subalgebra.range_valproof · cited by 9
- map_nhds_subtype_valproof · cited by 6
- Types.monoOverEquivalenceSetproof · cited by 6
- Module.finitePresentation_of_surjectiveproof · cited by 6
- Module.FinitePresentation.fg_kerproof · cited by 6
- Subtype.preconnectedSpaceproof · cited by 4
- Subring.isIntegrallyClosedIn_iffproof · cited by 3
- Module.projective_of_localization_maximalproof · cited by 3