File size: 1,839 Bytes
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 | import Mathlib
import OAI.Combinatorics.MatchingCount.Sampling.TreeOptions
import OAI.Combinatorics.MatchingCount.Machines.TreeSum
namespace OAI
namespace MatchingFPRAS.TreeTyped
open TreeData
variable {A B : Type} [Codec A] [Codec B]
lemma constantData_program (d : Data) :
(constantData (A:=A) d).program=(constantData (A:=B) d).program := by
induction d with
| nil=>rfl
| cons a b ih ihb=>
change TreeFunction.pair _ _ = TreeFunction.pair _ _
rw [ih,ihb]
lemma constant_program (a : A) (b : B) (h : encode a=encode b)
{C D : Type} [Codec C] [Codec D] :
(constant (A:=C) a).program=(constant (A:=D) b).program := by
change (constantData (A:=C) (encode a)).program=(constantData (A:=D) (encode b)).program
rw [h]
exact constantData_program _
lemma encode_empty_finset {E : Type} [Codec E] [LinearOrder E] :
encode (∅ : Finset E)=Data.nil := by
simp only [encode_finset,Finset.sort_empty,encode_list_nil]
lemma head_program (a : A) (b : B) (h : encode a=encode b) :
(head a).program=(head b).program := by
change RegisterStructured.select 0 (constant a).program first.program =
RegisterStructured.select 0 (constant b).program first.program
rw [constant_program a b h (C:=List A) (D:=List B)]
rfl
lemma getDFast_program (a : A) (b : B) (h : encode a=encode b) :
(getDFast a).program=(getDFast b).program := by
change RegisterProc.seq dropFast.program (head a).program =
RegisterProc.seq dropFast.program (head b).program
rw [head_program a b h]
rfl
lemma draw_program (a : A) (b : B) (h : encode a=encode b) :
(ExecutableOptions.drawRealizer a).program=(ExecutableOptions.drawRealizer b).program := by
unfold ExecutableOptions.drawRealizer
dsimp only [Realizer.congr, composition, pair]
rw [getDFast_program a b h]
rfl
end MatchingFPRAS.TreeTyped
end OAI
|