Theorems · Definition · group theory

IsAddCyclic.casesOn

{G : Type u} →
  [inst : SMul ℤ G] →
    {motive : IsAddCyclic G → Sort u_1} →
      (t : IsAddCyclic G) → ((exists_zsmul_surjective : ∃ g, Function.Surjective fun x => x • g) → motive ⋯) → motive t

Defined in: Mathlib.Algebra.Group.Defs
Cited by: 3 results in Mathlib
Foundations: Depth 6 from the axioms · uses no axioms
Assumes: SMul

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

IsAddCyclicstatement and proof · cited by 55

Cited by3

Results whose statement or proof uses this declaration.

isAddCyclic_of_surjectiveproof · cited by 5
LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_intproof · cited by 2
exists_nsmul_ne_zero_of_isAddCyclicproof · cited by 0