Theorems · Theorem · real analysis
Real.cos_neg_of_pi_div_two_lt_of_lt
∀ {x : ℝ}, Real.pi / 2 < x → x < Real.pi + Real.pi / 2 → Real.cos x < 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Real.cosstatement · cited by 424
- lt_of_not_geproof · cited by 374
- neg_posproof · cited by 74
- Real.cos_pos_of_mem_Iooproof · cited by 14
- Real.cos_pi_subproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Complex.arg_mul_cos_add_sin_mul_Iproof · cited by 5