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Theorems · Theorem · order theory

Set.Ioi_add_bij

∀ {M : Type u_1} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [IsOrderedCancelAddMonoid M] [ExistsAddOfLE M]
  (a d : M), Set.BijOn (fun x => x + d) (Set.Ioi a) (Set.Ioi (a + d))
Defined in
Mathlib.Algebra.Order.Interval.Set.Monoid
Cited by
3 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidPartialOrderIsOrderedCancelAddMonoidExistsAddOfLE
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Around this declaration

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

Set.Ioo_add_bij · cited by 1Set.Ioo_add_bijSet.Ioc_add_bij · cited by 1Set.Ioc_add_bijSet.image_add_const_Ioi · cited by 1Set.image_add_const_IoiAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderLT.lt.le · cited by 2189lt.leSet.Ioi · cited by 1463Set.IoiIsOrderedCancelAddMonoid · cited by 359IsOrderedCancelAddMonoidExistsAddOfLE · cited by 330ExistsAddOfLESet.BijOn · cited by 168Set.BijOnadd_right_comm · cited by 85add_right_commSet.mem_Ioi · cited by 80Set.mem_Ioiadd_lt_add_iff_right · cited by 42add_lt_add_iff_rightExistsAddOfLE.exists_add_of_le · cited by 42ExistsAddOfLE.exists_add_…Set.Ioi_add_bijCITED BYCITES

Cites11

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

Cited by3

Results whose statement or proof uses this declaration.