Theorems · Theorem · number theory

basisOfTopLeSpanOfCardEqFinrank.congr_simp

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : OrzechProperty R] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] {ι : Type u_3} [inst_4 : Fintype ι] (b b_1 : ι → M) (e_b : b = b_1)
  (le_span : ⊤ ≤ Submodule.span R (Set.range b)) (card_eq : Fintype.card ι = Module.finrank R M),
  basisOfTopLeSpanOfCardEqFinrank b le_span card_eq = basisOfTopLeSpanOfCardEqFinrank b_1 ⋯ card_eq

Defined in: Mathlib.Algebra.Module.ZLattice.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring OrzechProperty AddCommMonoid Module Fintype

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Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
Top.topstatement and proof · cited by 9,680
Fintypestatement and proof · cited by 7,736
Submodulestatement · cited by 7,192
Set.rangestatement and proof · cited by 4,705
Module.finrankstatement and proof · cited by 1,770
Submodule.spanstatement and proof · cited by 1,504
Module.Basisstatement · cited by 1,477
Fintype.cardstatement and proof · cited by 1,386
OrzechPropertystatement and proof · cited by 16

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