Theorems · Theorem · complex analysis
Real.exp_sub
∀ (x y : ℝ), Real.exp (x - y) = Real.exp x / Real.exp y
- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- sub_eq_add_negproof · cited by 1,023
- Real.expstatement and proof · cited by 871
- div_eq_mul_invproof · cited by 715
- Real.exp_addproof · cited by 39
- Real.exp_negproof · cited by 28
Cited by13
Results whose statement or proof uses this declaration.
- Real.log_divproof · cited by 21
- Real.tendsto_log_comp_add_sub_logproof · cited by 3
- Complex.norm_cpow_of_ne_zeroproof · cited by 2
- Behrend.exp_neg_two_mul_leproof · cited by 1
- Real.logDeriv_expproof · cited by 1
- UpperHalfPlane.im_le_im_mul_exp_distproof · cited by 1
- ProbabilityTheory.setIntegral_tilted_mul_eq_cgf'proof · cited by 0
- ProbabilityTheory.tilted_mul_apply_cgfproof · cited by 0
- ProbabilityTheory.tilted_mul_apply_cgf'proof · cited by 0
- ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgfproof · cited by 0
- ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf'proof · cited by 0
- ProbabilityTheory.integral_tilted_mul_eq_cgfproof · cited by 0