Theorems · Theorem · measure theory
intervalIntegral.integral_comp_sub_left
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} (f : ℝ → E) (d : ℝ),
∫ (x : ℝ) in a..b, f (d - x) = ∫ (x : ℝ) in d - b..d - a, f x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 261 from the axioms · uses propext, Classical.choice, 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.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- one_mulproof · cited by 2,841
- one_smulproof · cited by 1,374
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- one_ne_zeroproof · cited by 885
- intervalIntegralstatement and proof · cited by 546
- inv_oneproof · cited by 301
- intervalIntegral.integral_comp_sub_mulproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_comp_negproof · cited by 3
- EulerSine.integral_cos_pow_eqproof · cited by 2
- integral_log_sin_zero_pi_div_twoproof · cited by 1
- curveIntegral_symmproof · cited by 0