[Merged by Bors] - feat(order/sup_indep): Finite supremum independence #9867
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YaelDillies
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jcommelin
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Oct 25, 2021
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Can we add this lemma or a variant of it somewhere? lemma sup_indep_iff {α} [complete_distrib_lattice α] (s : finset ι) (f : ι → α) :
complete_lattice.independent (f ∘ (coe : s → ι)) ↔ sup_indep s f :=
begin
rw complete_lattice.independent, rw sup_indep,
refine subtype.forall.trans _,
refine forall_congr _,
intros a,
refine forall_congr _,
intros b,
rw finset.sup_eq_supr,
apply iff_of_eq,
congr' 1,
refine supr_subtype.trans _,
congr' 1 with x,
simp [supr_and],
rw supr_comm,
end |
eric-wieser
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Oct 27, 2021
eric-wieser
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Oct 28, 2021
eric-wieser
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Oct 28, 2021
bors bot
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Nov 4, 2021
…se_disjoint` (#9898) This will allow to express the bind operation: you can't currently express that the pairwise disjoint union of pairwise disjoint sets pairwise disjoint. Here's the corresponding statement with `finset.sup_indep` (defined in #9867): ```lean lemma sup_indep.sup {s : finset ι'} {g : ι' → finset ι} {f : ι → α} (hs : s.sup_indep (λ i, (g i).sup f)) (hg : ∀ i' ∈ s, (g i').sup_indep f) : (s.sup g).sup_indep f := ``` You currently can't do `set.pairwise_disjoint s (λ i, ⋃ x ∈ g i, f x)`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
bors bot
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Nov 4, 2021
…se_disjoint` (#9898) This will allow to express the bind operation: you can't currently express that the pairwise disjoint union of pairwise disjoint sets pairwise disjoint. Here's the corresponding statement with `finset.sup_indep` (defined in #9867): ```lean lemma sup_indep.sup {s : finset ι'} {g : ι' → finset ι} {f : ι → α} (hs : s.sup_indep (λ i, (g i).sup f)) (hg : ∀ i' ∈ s, (g i').sup_indep f) : (s.sup g).sup_indep f := ``` You currently can't do `set.pairwise_disjoint s (λ i, ⋃ x ∈ g i, f x)`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
fpvandoorn
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Nov 9, 2021
ericrbg
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Nov 9, 2021
…se_disjoint` (#9898) This will allow to express the bind operation: you can't currently express that the pairwise disjoint union of pairwise disjoint sets pairwise disjoint. Here's the corresponding statement with `finset.sup_indep` (defined in #9867): ```lean lemma sup_indep.sup {s : finset ι'} {g : ι' → finset ι} {f : ι → α} (hs : s.sup_indep (λ i, (g i).sup f)) (hg : ∀ i' ∈ s, (g i').sup_indep f) : (s.sup g).sup_indep f := ``` You currently can't do `set.pairwise_disjoint s (λ i, ⋃ x ∈ g i, f x)`. Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
eric-wieser
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Nov 13, 2021
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LGTM bors merge |
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Nov 15, 2021
This defines supremum independence of indexed finsets.
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This defines supremum independence of indexed finsets.
Note, this is currently very redundant with
set.pairwise_disjoint, both notions being equivalent in distributive lattices. The expectation is that we'll be able to talk about disjointness and sup (simultaneously!) in non distributive lattices sometimes soon.