Mathlib Map

Theorems · Theorem · group theory

add_sub_cancel_left

∀ {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + b - a = b
Defined in
Mathlib.Algebra.Group.Basic
Cited by
198 results in Mathlib
Foundations
Depth 13 from the axioms, rests on 69 definitions · uses propext
Assumes
AddCommGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

add_sub_cancel · cited by 195add_sub_cancelmeromorphicOrderAt_eq_int_iff · cited by 31meromorphicOrderAt_eq_int…sub_add_cancel_left · cited by 19sub_add_cancel_leftadd_sub_sub_cancel · cited by 14add_sub_sub_cancelcircleMap_sub_center · cited by 12circleMap_sub_centerHasFPowerSeriesOnBall.congr · cited by 9HasFPowerSeriesOnBall.con…tendstoUniformlyOn_tsum · cited by 9tendstoUniformlyOn_tsumNormedSpace.sphere_nonempty · cited by 8NormedSpace.sphere_nonemp…hasFDerivAt_iff_isLittleO_nhds_zero · cited by 7hasFDerivAt_iff_isLittleO…Real.volume_ball · cited by 6Real.volume_ballReal.Icc_eq_closedBall · cited by 6Real.Icc_eq_closedBallmidpoint_eq_smul_add · cited by 6midpoint_eq_smul_addtendstoUniformlyOn_tsum_of_cofinite_eventually · cited by 6tendstoUniformlyOn_tsum_o…Real.rpowIntegrand₀₁_eq_pow_div · cited by 6Real.rpowIntegrand₀₁_eq_p…QuadraticMap.polar_smul_left · cited by 5QuadraticMap.polar_smul_l…AddCommGroup · cited by 12871AddCommGroupneg_add_cancel_left · cited by 84neg_add_cancel_leftsub_eq_neg_add · cited by 51sub_eq_neg_addadd_sub_cancel_leftCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by198

Results whose statement or proof uses this declaration.