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e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | import Mathlib
import OAI.Combinatorics.MatchingCount.Sampling.Relabel
namespace OAI
namespace MatchingFPRAS.RationalSource
open MatchingFPRAS Switching Subdivision RealGeometry Hierarchy Enlargement Transport Finset
variable {V : Type*} [Fintype V] [LinearOrder V] [Nontrivial V]
attribute [local instance] NumberedHierarchy.labelOrder sym2Order bagEdgeOrder bagEdgeFintype
attribute [local instance] UnitRefresh.Computable.allowedDec prodOrder sumOrder
lemma labelCast_level {X : Type*} [Fintype X] {B B' : X → X → ℝ}
(s : ∀ x y,B x y=B y x)
(t : ∀ x y z,x≠y → x≠z → y≠z → min (B x z) (B z y)≤B x y)
(s' : ∀ x y,B' x y=B' y x)
(t' : ∀ x y z,x≠y → x≠z → y≠z → min (B' x z) (B' z y)≤B' x y)
{H H' : ℕ} (hB : B=B') (hH : H=H') (l : Hierarchy.Label B s t H) :
(labelCast s t s' t' hB hH l).1.val=l.1.val := by
cases hB;cases hH;rfl
lemma labelCast_edgeLabel {X E : Type*} [Fintype X] [DecidableEq X] [Fintype E]
{B B' : X → X → ℝ}
(s : ∀ x y,B x y=B y x)
(t : ∀ x y z,x≠y → x≠z → y≠z → min (B x z) (B z y)≤B x y)
(s' : ∀ x y,B' x y=B' y x)
(t' : ∀ x y z,x≠y → x≠z → y≠z → min (B' x z) (B' z y)≤B' x y)
(u v : E → X) {H H' : ℕ} (hB : B=B') (hH : H=H') (e : E) :
labelCast s t s' t' hB hH (Hierarchy.edgeLabel B s t u v H e)=
Hierarchy.edgeLabel B' s' t' u v H' e := by
cases hB;cases hH;rfl
lemma labelsEquiv_level (w : V → V → ℚ) (K : ℕ)
(l : SourceLabel (fun x y=>(w x y:ℝ)) K) :
(labelsEquiv w K l).1.val=l.1.val := by
unfold labelsEquiv
simp only [Equiv.trans_apply,NumberedHierarchy.labelEquiv_level,labelCast_level]
lemma labelsEquiv_edgeLabel (w : V → V → ℚ) (K : ℕ) (q : SourceRealEdge V K) :
labelsEquiv w K (Hierarchy.edgeLabel (sourceRealB (fun x y=>(w x y:ℝ)) K)
(sourceRealB_comm _ _) (sourceRealB_tri _ _) (realLeft K) (realRight K)
(sourceLevels (fun x y=>(w x y:ℝ)) K) q)=realLabel w K q := by
unfold labelsEquiv
simp only [Equiv.trans_apply,labelCast_edgeLabel,NumberedHierarchy.edgeLabel_equiv,realLabel]
end MatchingFPRAS.RationalSource
end OAI
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