Theorems · Theorem · functional analysis
RCLike.lt_iff_re_im
∀ {K : Type u_1} [inst : RCLike K] {z w : K}, z < w ↔ RCLike.re z < RCLike.re w ∧ RCLike.im z = RCLike.im w- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- RCLike.imstatement and proof · cited by 161
- RCLike.toPartialOrderstatement · cited by 106
- RCLike.le_iff_re_improof · cited by 11
- RCLike.extproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- RCLike.pos_iffproof · cited by 4
- RCLike.neg_iffproof · cited by 2
- RCLike.ofReal_lt_ofRealproof · cited by 2
- RCLike.toIsStrictOrderedRingproof · cited by 0