Theorems · Theorem · Lie groups
Real.Angle.induction_on
∀ {p : Real.Angle → Prop} (θ : Real.Angle), (∀ (x : ℝ), p ↑x) → p θAn induction principle to deduce results for Angle from those for ℝ, used with
induction θ using Real.Angle.induction_on.
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Real.Anglestatement and proof · cited by 518
- Real.Angle.coestatement and proof · cited by 360
- Quotient.inductionOn'proof · cited by 69
Cited by29
Results whose statement or proof uses this declaration.
- Real.Angle.coe_toRealproof · cited by 11
- Real.Angle.toReal_le_piproof · cited by 6
- Real.Angle.neg_pi_lt_toRealproof · cited by 4
- Real.Angle.toReal_injectiveproof · cited by 4
- Real.Angle.sin_negproof · cited by 4
- Real.Angle.coe_toCircleproof · cited by 3
- Complex.arg_mul_cos_add_sin_mul_I_coe_angleproof · cited by 2
- Real.Angle.tan_periodicproof · cited by 2
- Real.Angle.arg_toCircleproof · cited by 2
- Real.Angle.sin_addproof · cited by 2
- Real.Angle.sin_antiperiodicproof · cited by 2
- Real.Angle.cos_antiperiodicproof · cited by 2