Theorems · Theorem · commutative algebra

Module.Presentation.finsupp_relation

∀ {A : Type u} [inst : Ring A] {N : Type v} [inst_1 : AddCommGroup N] [inst_2 : Module A N]
  (pres : Module.Presentation A N) (ι : Type w) [inst_3 : DecidableEq ι] [inst_4 : DecidableEq N]
  (x : (i : ι) × ((fun i => ((fun x => pres) i).toRelations) i).R),
  (pres.finsupp ι).relation x = Finsupp.embDomain (Function.Embedding.sigmaMk x.fst) (pres.relation x.snd)

Defined in: Mathlib.Algebra.Module.Presentation.DirectSum
Cited by: 0 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup Module DecidableEq DecidableEq

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Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
Finsuppstatement · cited by 5,255
Module.Relations.Gstatement · cited by 103
Finsupp.embDomainstatement · cited by 69
Module.Relations.Rstatement and proof · cited by 57
Module.Presentation.toRelationsstatement and proof · cited by 49
Module.Presentationstatement and proof · cited by 40
Module.Relations.relationstatement and proof · cited by 38
Function.Embedding.sigmaMkstatement · cited by 25
Module.Presentation.finsuppstatement and proof · cited by 4

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