Theorems · Theorem · field theory
Complex.reProdIm_subset_iff
∀ {s s₁ t t₁ : Set ℝ}, s ×ℂ t ⊆ s₁ ×ℂ t₁ ↔ s ×ˢ t ⊆ s₁ ×ˢ t₁The inequality s × t ⊆ s₁ × t₁ holds in ℂ iff it holds in ℝ × ℝ.
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
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.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Set.preimageproof · cited by 4,946
- SProd.sprodstatement and proof · cited by 1,750
- Complex.reProdImstatement and proof · cited by 39
- Complex.equivRealProdproof · cited by 15
- Complex.preimage_equivRealProd_prodproof · cited by 3
- Equiv.preimage_subsetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Complex.reProdIm_subset_iff'proof · cited by 0