Theorems · Theorem · order theory
Function.Surjective.iSup_comp
∀ {α : Type u_1} {ι : Sort u_4} {ι' : Sort u_5} [inst : SupSet α] {f : ι → ι'},
Function.Surjective f → ∀ (g : ι' → α), ⨆ x, g (f x) = ⨆ y, g y- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
- Assumes
- SupSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.rangeproof · cited by 4,705
- iSupstatement · cited by 2,415
- SupSet.sSupproof · cited by 954
- SupSetstatement and proof · cited by 154
- Function.Surjective.range_compproof · cited by 18
Cited by9
Results whose statement or proof uses this declaration.
- Equiv.iSup_compproof · cited by 14
- Function.Surjective.iSup_congrproof · cited by 14
- Function.Surjective.iUnion_compproof · cited by 10
- iSup_unpairproof · cited by 3
- iSup_eq_iSup_finset'proof · cited by 1
- MeasureTheory.IsSetSemiring.sUnion_disjointOfUnionproof · cited by 1
- IsNonarchimedean.iSup_abv_linearMap_apply_leproof · cited by 1
- iSupIndep.comp'proof · cited by 1
- Set.exists_seq_iSup_eq_top_iff_countableproof · cited by 1