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Theorems · Theorem · group theory

Finset.Nontrivial.mul_left

∀ {α : Type u_2} [inst : Mul α] [IsLeftCancelMul α] [inst_2 : DecidableEq α] {s t : Finset α},
  t.Nontrivial → s.Nonempty → (s * t).Nontrivial
Defined in
Mathlib.Algebra.Group.Pointwise.Finset.Basic
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulIsLeftCancelMulDecidableEq
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.Nontrivial.mul · cited by 0Nontrivial.mulFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeFinset.Nonempty · cited by 1001Finset.NonemptyFinset.mul · cited by 155Finset.mulFinset.Nontrivial · cited by 53Finset.NontrivialIsLeftCancelMul · cited by 51IsLeftCancelMulFinset.mul_mem_mul · cited by 14Finset.mul_mem_mulNontrivial.mul_leftCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.