Theorems · Theorem · functional analysis
isQuasiregular_iff
∀ {R : Type u_1} [inst : NonUnitalSemiring R] {x : R}, IsQuasiregular x ↔ ∃ y, y + x + x * y = 0 ∧ x + y + y * x = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- NonUnitalSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equiv.symmproof · cited by 3,681
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- Equiv.injectiveproof · cited by 464
- NonUnitalSemiringstatement and proof · cited by 339
- IsQuasiregularstatement and proof · cited by 18
- PreQuasiregularproof · cited by 18
- PreQuasiregular.equivproof · cited by 11
- PreQuasiregular.add_inv_add_mul_eq_zeroproof · cited by 1
- PreQuasiregular.equiv_symm_applyproof · cited by 1
- PreQuasiregular.inv_add_add_mul_eq_zeroproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Unitization.isQuasiregular_inr_iffproof · cited by 2
- IsQuasiregular.mapproof · cited by 2
- IsQuasiregular.isUnit_one_addproof · cited by 1
- isQuasiregular_iff_isUnitproof · cited by 1