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Theorems · Theorem · group theory

AddCommGroup.ModEq.add

∀ {M : Type u_1} [inst : AddCommMonoid M] {a b c d p : M}, a ≡ b [PMOD p] → c ≡ d [PMOD p] → a + c ≡ b + d [PMOD p]
Defined in
Mathlib.Algebra.Group.ModEq
Cited by
3 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.add_iff_left · cited by 3ModEq.add_iff_leftAddCommGroup.ModEq.add_left · cited by 0ModEq.add_leftAddCommGroup.ModEq.add_right · cited by 0ModEq.add_rightAddCommMonoid · cited by 12281AddCommMonoidAddCommGroup.ModEq · cited by 107AddCommGroup.ModEqadd_add_add_comm · cited by 56add_add_add_commadd_nsmul · cited by 44add_nsmulAddCommGroup.modEq_iff_nsmul · cited by 11AddCommGroup.modEq_iff_ns…ModEq.addCITED BYCITES

Cites5

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Cited by3

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