Theorems · Theorem · commutative algebra

HahnSeries.SummableFamily.smul.congr_simp

∀ {Γ : Type u_1} {Γ' : Type u_2} {R : Type u_3} {V : Type u_4} {α : Type u_5} {β : Type u_6} [inst : PartialOrder Γ]
  [inst_1 : PartialOrder Γ'] [inst_2 : AddCommMonoid V] [inst_3 : AddCommMonoid R] [inst_4 : SMulWithZero R V]
  [inst_5 : VAdd Γ Γ'] [inst_6 : IsOrderedCancelVAdd Γ Γ'] (s s_1 : HahnSeries.SummableFamily Γ R α),
  s = s_1 → ∀ (t t_1 : HahnSeries.SummableFamily Γ' V β), t = t_1 → s.smul t = s_1.smul t_1

Defined in

Mathlib.RingTheory.HahnSeries.Summable

Cited by

0 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderAddCommMonoidAddCommMonoidSMulWithZeroVAddIsOrderedCancelVAdd