Theorems · Theorem · order theory

Set.preimage_mul_const_Ici_of_neg

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] (a : α) {c : α},
  c < 0 → (fun x => x * c) ⁻¹' Set.Ici a = Set.Iic (a / c)

Defined in: Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by: 3 results in Mathlib
Foundations: Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field LinearOrder IsStrictOrderedRing

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Cites9

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

Setstatement · cited by 53,352
LinearOrderstatement and proof · cited by 8,572
Fieldstatement and proof · cited by 7,404
Set.preimagestatement · cited by 4,946
IsStrictOrderedRingstatement and proof · cited by 2,490
Set.extproof · cited by 2,266
Set.Iicstatement · cited by 1,111
Set.Icistatement · cited by 1,070
le_div_iff_of_negproof · cited by 3

Cited by3

Results whose statement or proof uses this declaration.

Set.preimage_mul_const_Icc_of_negproof · cited by 2
Set.preimage_mul_const_Ico_of_negproof · cited by 1
Set.preimage_const_mul_Ici_of_negproof · cited by 0