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Theorems · Theorem · order theory

Finset.prod_Iic_add_one_comm

∀ {α : Type u_1} {M : Type u_2} [inst : CommMonoid M] [inst_1 : LinearOrder α] [inst_2 : LocallyFiniteOrderBot α]
  [inst_3 : Add α] [inst_4 : One α] [SuccAddOrder α] [NoMaxOrder α] (a : α) (f : α → M),
  ∏ i ≤ a + 1, f i = f (a + 1) * ∏ i ≤ a, f i
Defined in
Mathlib.Algebra.Order.BigOperators.Group.LocallyFinite
Cited by
1 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidLinearOrderLocallyFiniteOrderBotAddOneSuccAddOrderNoMaxOrder
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Around this declaration

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

Finset.prod_Iic_add_one · cited by 0Finset.prod_Iic_add_oneLinearOrder · cited by 8572LinearOrderFinset.prod · cited by 2356Finset.prodCommMonoid · cited by 2264CommMonoidFinset.prod_congr · cited by 646Finset.prod_congrNoMaxOrder · cited by 340NoMaxOrderLocallyFiniteOrderBot · cited by 286LocallyFiniteOrderBotFinset.Iic · cited by 280Finset.IicFinset.Iio · cited by 147Finset.IioFinset.prod_insert · cited by 109Finset.prod_insertSuccAddOrder · cited by 108SuccAddOrderFinset.prod_Iio_add_one_comm · cited by 2Finset.prod_Iio_add_one_c…Finset.prod_Iic_add_one_commCITED BYCITES

Cites11

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Cited by1

Results whose statement or proof uses this declaration.