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Theorems · Theorem · group theory

AddCommGroup.ModEq.trans

∀ {M : Type u_1} [inst : AddCommMonoid M] {a b c p : M}, a ≡ b [PMOD p] → b ≡ c [PMOD p] → a ≡ c [PMOD p]
Defined in
Mathlib.Algebra.Group.ModEq
Cited by
5 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
AddCommMonoid
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Around this declaration

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

AddCommGroup.modEq_iff_natModEq · cited by 1AddCommGroup.modEq_iff_na…AddCommGroup.ModEq.nsmul_add · cited by 0ModEq.nsmul_addAddCommGroup.ModEq.add_nsmul · cited by 0ModEq.add_nsmulAddCommGroup.ModEq.zsmul_add · cited by 0ModEq.zsmul_addAddCommGroup.ModEq.add_zsmul · cited by 0ModEq.add_zsmulAddCommMonoid · cited by 12281AddCommMonoidadd_assoc · cited by 746add_assocAddCommGroup.ModEq · cited by 107AddCommGroup.ModEqadd_left_comm · cited by 76add_left_commadd_nsmul · cited by 44add_nsmulAddCommGroup.modEq_iff_nsmul · cited by 11AddCommGroup.modEq_iff_ns…ModEq.transCITED BYCITES

Cites6

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Cited by5

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