Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files
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 Community
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2.09M
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/LinalgSemantics.lean
mapMCommute.mapM_commute
[282, 1]
[312, 2]
congr
case e_a.h m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : fish (mapM f) (mapM g) ...
case e_a.h.e_a m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : fish (mapM f) (mapM...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/LinalgSemantics.lean
mapMCommute.mapM_commute
[282, 1]
[312, 2]
funext x'
case e_a.h.e_a m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : fish (mapM f) (mapM...
case e_a.h.e_a.h m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : fish (mapM f) (ma...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/LinalgSemantics.lean
mapMCommute.mapM_commute
[282, 1]
[312, 2]
simp [fish] at IH
case e_a.h.e_a.h m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : fish (mapM f) (ma...
case e_a.h.e_a.h m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : mapM f tail >>= m...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/LinalgSemantics.lean
mapMCommute.mapM_commute
[282, 1]
[312, 2]
rewrite [<- IH]
case e_a.h.e_a.h m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : mapM f tail >>= m...
case e_a.h.e_a.h m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : mapM f tail >>= m...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/LinalgSemantics.lean
mapMCommute.mapM_commute
[282, 1]
[312, 2]
simp[bind_assoc]
case e_a.h.e_a.h m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : mapM f tail >>= m...
case e_a.h.COMMUTE m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : fish (mapM f) (...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/LinalgSemantics.lean
mapMCommute.mapM_commute
[282, 1]
[312, 2]
apply COMMUTE
case e_a.h.COMMUTE m : Type β†’ Type u_1 a : Type M : Monad m LM : LawfulMonad m f g : a β†’ m a COMMUTE : βˆ€ {b : Type} (x y : a) (k : a β†’ a β†’ m b), (do let r1 ← f x let r2 ← g y k r1 r2) = do let r2 ← g y let r1 ← f x k r1 r2 head : a tail : List a IH : fish (mapM f) (...
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Examples/IfStatementOptimization.lean
SCF_SELECT.equivalent
[38, 1]
[63, 55]
simp [LHS, RHS, INPUT]
b : FinInt 1 n m : FinInt 32 ⊒ run (denoteOp Ξ” LHS) (INPUT b n m) = run (denoteOp Ξ” RHS) (INPUT b n m)
b : FinInt 1 n m : FinInt 32 ⊒ run (denoteOp Ξ” (Op.mk "scf.if" [(SSAVal.SSAVal "x", MLIRType.int Signedness.Signless 32)] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [Region.mk "entry" [] [Op.mk "scf.yield" [] [(SSAVal.SSAVal "n", MLIRType.int Signedness.Sig...
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/02Equality.lean
reverse_mkSymm
[81, 1]
[83, 16]
simp [mkSymm]
α : Type u_1 xs : List α ⊒ List.reverse (mkSymm xs) = mkSymm xs
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.one_add_add
[35, 1]
[40, 12]
induction n with | zero => rfl | succ n ih => dsimp congr 1
m n : MyNat ⊒ m + 1 + n = m + n + 1
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.one_add_add
[35, 1]
[40, 12]
rfl
case zero m : MyNat ⊒ m + 1 + zero = m + zero + 1
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.one_add_add
[35, 1]
[40, 12]
dsimp
case succ m n : MyNat ih : m + 1 + n = m + n + 1 ⊒ m + 1 + succ n = m + succ n + 1
case succ m n : MyNat ih : m + 1 + n = m + n + 1 ⊒ m + 1 + n + 1 = m + n + 1 + 1
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.one_add_add
[35, 1]
[40, 12]
congr 1
case succ m n : MyNat ih : m + 1 + n = m + n + 1 ⊒ m + 1 + n + 1 = m + n + 1 + 1
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.zero_add
[43, 1]
[48, 12]
induction m with | zero => dsimp | succ m ih => dsimp rw [ih]
m : MyNat ⊒ 0 + m = m
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.zero_add
[43, 1]
[48, 12]
dsimp
case zero ⊒ 0 + zero = zero
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.zero_add
[43, 1]
[48, 12]
dsimp
case succ m : MyNat ih : 0 + m = m ⊒ 0 + succ m = succ m
case succ m : MyNat ih : 0 + m = m ⊒ 0 + m + 1 = m + 1
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.zero_add
[43, 1]
[48, 12]
rw [ih]
case succ m : MyNat ih : 0 + m = m ⊒ 0 + m + 1 = m + 1
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_assoc
[50, 1]
[53, 27]
induction o with | zero => simp | succ o ih => simp [ih]
m n o : MyNat ⊒ m + (n + o) = m + n + o
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_assoc
[50, 1]
[53, 27]
simp
case zero m n : MyNat ⊒ m + (n + zero) = m + n + zero
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_assoc
[50, 1]
[53, 27]
simp [ih]
case succ m n o : MyNat ih : m + (n + o) = m + n + o ⊒ m + (n + succ o) = m + n + succ o
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_comm
[55, 1]
[63, 12]
induction n with | zero => dsimp rw [zero_add] | succ n ih => dsimp rw [one_add_add] rw [ih]
m n : MyNat ⊒ m + n = n + m
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_comm
[55, 1]
[63, 12]
dsimp
case zero m : MyNat ⊒ m + zero = zero + m
case zero m : MyNat ⊒ m = 0 + m
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_comm
[55, 1]
[63, 12]
rw [zero_add]
case zero m : MyNat ⊒ m = 0 + m
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_comm
[55, 1]
[63, 12]
dsimp
case succ m n : MyNat ih : m + n = n + m ⊒ m + succ n = succ n + m
case succ m n : MyNat ih : m + n = n + m ⊒ m + n + 1 = n + 1 + m
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_comm
[55, 1]
[63, 12]
rw [one_add_add]
case succ m n : MyNat ih : m + n = n + m ⊒ m + n + 1 = n + 1 + m
case succ m n : MyNat ih : m + n = n + m ⊒ m + n + 1 = n + m + 1
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/06Induction.lean
MyNat.add_comm
[55, 1]
[63, 12]
rw [ih]
case succ m n : MyNat ih : m + n = n + m ⊒ m + n + 1 = n + m + 1
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/10Aesop.lean
ne_nil_of_mem
[8, 1]
[9, 8]
aesop
Ξ± : Type u_1 a : Ξ± l : List Ξ± h : a ∈ l ⊒ l β‰  []
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/10Aesop.lean
not_mem_cons_of_ne_of_not_mem
[11, 1]
[13, 8]
aesop
Ξ± : Type u_1 a y : Ξ± l : List Ξ± ⊒ a β‰  y β†’ Β¬a ∈ l β†’ Β¬a ∈ y :: l
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/10Aesop.lean
mem_map
[15, 9]
[17, 24]
induction l <;> aesop
Ξ± : Type u_1 Ξ² : Type u_2 f : Ξ± β†’ Ξ² b : Ξ² l : List Ξ± ⊒ b ∈ List.map f l ↔ βˆƒ a, a ∈ l ∧ f a = b
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/10Aesop.lean
mem_map_of_mem
[20, 1]
[22, 8]
aesop
Ξ± : Type u_1 Ξ² : Type u_2 f : Ξ± β†’ Ξ² a : Ξ± l : List Ξ± h : a ∈ l ⊒ f a ∈ List.map f l
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/10Aesop.lean
eq_nil_of_subset_nil
[25, 1]
[26, 28]
aesop (add 1% cases List)
Ξ± : Type u_1 l : List Ξ± ⊒ l βŠ† [] β†’ l = []
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.foo
[57, 1]
[62, 26]
intro legal
p : Piece n✝ : β„• start stop : Pos n✝ ⊒ Piece.LegalMove start stop p β†’ start β‰  stop
p : Piece n✝ : β„• start stop : Pos n✝ legal : Piece.LegalMove start stop p ⊒ start β‰  stop
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.foo
[57, 1]
[62, 26]
cases legal with | rookHorizontal h _ => exact h | rookVertical h _ => exact h | king h _ _ => exact h
p : Piece n✝ : β„• start stop : Pos n✝ legal : Piece.LegalMove start stop p ⊒ start β‰  stop
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.foo
[57, 1]
[62, 26]
exact h
case rookHorizontal n✝ : β„• start stop : Pos n✝ h : start β‰  stop a✝ : start.y = stop.y ⊒ start β‰  stop
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.foo
[57, 1]
[62, 26]
exact h
case rookVertical n✝ : β„• start stop : Pos n✝ h : start β‰  stop a✝ : start.x = stop.x ⊒ start β‰  stop
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.foo
[57, 1]
[62, 26]
exact h
case king n✝ : β„• start stop : Pos n✝ h : start β‰  stop a✝¹ : Nat.dist ↑start.x ↑stop.x ≀ 1 a✝ : Nat.dist ↑start.y ↑stop.y ≀ 1 ⊒ start β‰  stop
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.Board.set_same
[105, 1]
[106, 13]
simp [set]
n : β„• pos : Pos n p? : Option PPiece b : Board n ⊒ set b pos p? pos = p?
no goals
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.Board.set_different
[108, 1]
[112, 11]
intro h
n : β„• pos' pos : Pos n p? : Option PPiece b : Board n ⊒ pos' β‰  pos β†’ set b pos p? pos' = b pos'
n : β„• pos' pos : Pos n p? : Option PPiece b : Board n h : pos' β‰  pos ⊒ set b pos p? pos' = b pos'
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.Board.set_different
[108, 1]
[112, 11]
simp [set]
n : β„• pos' pos : Pos n p? : Option PPiece b : Board n h : pos' β‰  pos ⊒ set b pos p? pos' = b pos'
n : β„• pos' pos : Pos n p? : Option PPiece b : Board n h : pos' β‰  pos ⊒ pos = pos' β†’ p? = b pos'
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.Board.set_different
[108, 1]
[112, 11]
intros
n : β„• pos' pos : Pos n p? : Option PPiece b : Board n h : pos' β‰  pos ⊒ pos = pos' β†’ p? = b pos'
n : β„• pos' pos : Pos n p? : Option PPiece b : Board n h : pos' β‰  pos a✝ : pos = pos' ⊒ p? = b pos'
https://github.com/JLimperg/regensburg-itp-school-2023.git
7307618fa6d85c090896d29021541cd67920d750
Talk/11MiniChess.lean
MiniChess.Board.set_different
[108, 1]
[112, 11]
simp_all
n : β„• pos' pos : Pos n p? : Option PPiece b : Board n h : pos' β‰  pos a✝ : pos = pos' ⊒ p? = b pos'
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.no_nbhrs
[50, 1]
[56, 40]
contrapose! hA
α : Type u_1 inst✝¹ : Fintype α inst✝ : DecidableEq α v w : α M : MultiPart α hA : ¬v ∈ M.A ⊒ ¬Adj (mp M) v w
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± v w : Ξ± M : MultiPart Ξ± hA : βˆƒ i, i ∈ range (M.t + 1) ∧ βˆƒ j, j ∈ range (M.t + 1) ∧ i β‰  j ∧ (v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j ∨ v ∈ MultiPart.P M j ∧ w ∈ MultiPart.P M i) ⊒ v ∈ M.A
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.no_nbhrs
[50, 1]
[56, 40]
obtain ⟨i, hi, j, hj, _, hv⟩ := hA
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± v w : Ξ± M : MultiPart Ξ± hA : βˆƒ i, i ∈ range (M.t + 1) ∧ βˆƒ j, j ∈ range (M.t + 1) ∧ i β‰  j ∧ (v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j ∨ v ∈ MultiPart.P M j ∧ w ∈ MultiPart.P M i) ⊒ v ∈ M.A
case intro.intro.intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± v w : Ξ± M : MultiPart Ξ± i : β„• hi : i ∈ range (M.t + 1) j : β„• hj : j ∈ range (M.t + 1) left✝ : i β‰  j hv : v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j ∨ v ∈ MultiPart.P M j ∧ w ∈ MultiPart.P M i ⊒ v ∈ M.A
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.no_nbhrs
[50, 1]
[56, 40]
cases hv with | inl hv => exact (sub_part hi) hv.1 | inr hv => exact (sub_part hj) hv.1
case intro.intro.intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± v w : Ξ± M : MultiPart Ξ± i : β„• hi : i ∈ range (M.t + 1) j : β„• hj : j ∈ range (M.t + 1) left✝ : i β‰  j hv : v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j ∨ v ∈ MultiPart.P M j ∧ w ∈ MultiPart.P M i ⊒ v ∈ M.A
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.no_nbhrs
[50, 1]
[56, 40]
exact (sub_part hi) hv.1
case intro.intro.intro.intro.intro.inl Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± v w : Ξ± M : MultiPart Ξ± i : β„• hi : i ∈ range (M.t + 1) j : β„• hj : j ∈ range (M.t + 1) left✝ : i β‰  j hv : v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j ⊒ v ∈ M.A
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.no_nbhrs
[50, 1]
[56, 40]
exact (sub_part hj) hv.1
case intro.intro.intro.intro.intro.inr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± v w : Ξ± M : MultiPart Ξ± i : β„• hi : i ∈ range (M.t + 1) j : β„• hj : j ∈ range (M.t + 1) left✝ : i β‰  j hv : v ∈ MultiPart.P M j ∧ w ∈ MultiPart.P M i ⊒ v ∈ M.A
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhrs_imp
[59, 1]
[62, 22]
intro h1
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± v w : Ξ± M : MultiPart Ξ± ⊒ Adj (mp M) v w β†’ v ∈ M.A
α : Type u_1 inst✝¹ : Fintype α inst✝ : DecidableEq α v w : α M : MultiPart α h1 : Adj (mp M) v w ⊒ v ∈ M.A
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhrs_imp
[59, 1]
[62, 22]
by_contra h
α : Type u_1 inst✝¹ : Fintype α inst✝ : DecidableEq α v w : α M : MultiPart α h1 : Adj (mp M) v w ⊒ v ∈ M.A
α : Type u_1 inst✝¹ : Fintype α inst✝ : DecidableEq α v w : α M : MultiPart α h1 : Adj (mp M) v w h : ¬v ∈ M.A ⊒ False
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhrs_imp
[59, 1]
[62, 22]
exact no_nbhrs h h1
α : Type u_1 inst✝¹ : Fintype α inst✝ : DecidableEq α v w : α M : MultiPart α h1 : Adj (mp M) v w h : ¬v ∈ M.A ⊒ False
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
intro h
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j ⊒ Adj (mp M) v w β†’ i β‰  j
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j h : Adj (mp M) v w ⊒ i β‰  j
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
cases' h with a ha
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j h : Adj (mp M) v w ⊒ i β‰  j
case intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• ha : a ∈ range (M.t + 1) ∧ βˆƒ j, j ∈ range (M.t + 1) ∧ a β‰  j ∧ (v ∈ MultiPart.P M a ∧ w ∈ MultiP...
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
obtain ⟨har, b, hbr, abne, ab⟩ := ha
case intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• ha : a ∈ range (M.t + 1) ∧ βˆƒ j, j ∈ range (M.t + 1) ∧ a β‰  j ∧ (v ∈ MultiPart.P M a ∧ w ∈ MultiP...
case intro.intro.intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPart.P...
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
cases ab with | inl ab => have ai := uniq_part hi har hvi ab.1; have bj := uniq_part hj hbr hwj ab.2 rwa [← ai, ← bj] at abne | inr ab => have aj := uniq_part hj har hwj ab.2; have bi := uniq_part hi hbr hvi ab.1 rw [← aj, ← bi] at abne exact abne.symm
case intro.intro.intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPart.P...
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
have ai := uniq_part hi har hvi ab.1
case intro.intro.intro.intro.intro.inl Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
case intro.intro.intro.intro.intro.inl Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
have bj := uniq_part hj hbr hwj ab.2
case intro.intro.intro.intro.intro.inl Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
case intro.intro.intro.intro.intro.inl Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
rwa [← ai, ← bj] at abne
case intro.intro.intro.intro.intro.inl Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
have aj := uniq_part hj har hwj ab.2
case intro.intro.intro.intro.intro.inr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
case intro.intro.intro.intro.intro.inr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
have bi := uniq_part hi hbr hvi ab.1
case intro.intro.intro.intro.intro.inr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
case intro.intro.intro.intro.intro.inr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
rw [← aj, ← bi] at abne
case intro.intro.intro.intro.intro.inr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : a β‰  b ab : v ∈ MultiPa...
case intro.intro.intro.intro.intro.inr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : j β‰  i ab : v ∈ MultiPa...
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_adj_imp
[65, 1]
[77, 20]
exact abne.symm
case intro.intro.intro.intro.intro.inr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j a : β„• har : a ∈ range (M.t + 1) b : β„• hbr : b ∈ range (M.t + 1) abne : j β‰  i ab : v ∈ MultiPa...
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_imp_adj
[80, 1]
[82, 64]
intro h
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j ⊒ i β‰  j β†’ Adj (mp M) v w
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j h : i β‰  j ⊒ Adj (mp M) v w
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_imp_adj
[80, 1]
[82, 64]
refine' ⟨i, hi, j, hj, h, _⟩
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j h : i β‰  j ⊒ Adj (mp M) v w
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j h : i β‰  j ⊒ v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j ∨ v ∈ MultiPart.P M j ∧ w ∈ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_imp_adj
[80, 1]
[82, 64]
left
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j h : i β‰  j ⊒ v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j ∨ v ∈ MultiPart.P M j ∧ w ∈ MultiPart.P M i
case h Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j h : i β‰  j ⊒ v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_imp_adj
[80, 1]
[82, 64]
exact ⟨hvi, hwj⟩
case h Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i j : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hj : j ∈ range (M.t + 1) hvi : v ∈ MultiPart.P M i hwj : w ∈ MultiPart.P M j h : i β‰  j ⊒ v ∈ MultiPart.P M i ∧ w ∈ MultiPart.P M j
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.not_nbhr_same_part
[85, 1]
[89, 38]
intro h1
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i ⊒ Adj (mp M) v w β†’ Β¬w ∈ MultiPart.P M i
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i h1 : Adj (mp M) v w ⊒ Β¬w ∈ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.not_nbhr_same_part
[85, 1]
[89, 38]
by_contra h
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i h1 : Adj (mp M) v w ⊒ Β¬w ∈ MultiPart.P M i
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i h1 : Adj (mp M) v w h : w ∈ MultiPart.P M i ⊒ False
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.not_nbhr_same_part
[85, 1]
[89, 38]
apply mp_adj_imp hi hi hv h h1
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i h1 : Adj (mp M) v w h : w ∈ MultiPart.P M i ⊒ False
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i h1 : Adj (mp M) v w h : w ∈ MultiPart.P M i ⊒ i = i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.not_nbhr_same_part
[85, 1]
[89, 38]
rfl
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i h1 : Adj (mp M) v w h : w ∈ MultiPart.P M i ⊒ i = i
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.not_nbhr_same_part'
[92, 1]
[96, 36]
intro h1
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hw : w ∈ MultiPart.P M i ⊒ Β¬Adj (mp M) v w
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hw : w ∈ MultiPart.P M i h1 : Adj (mp M) v w ⊒ False
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.not_nbhr_same_part'
[92, 1]
[96, 36]
contrapose hw
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hw : w ∈ MultiPart.P M i h1 : Adj (mp M) v w ⊒ False
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i h1 : Adj (mp M) v w hw : Β¬False ⊒ Β¬w ∈ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.not_nbhr_same_part'
[92, 1]
[96, 36]
exact not_nbhr_same_part hi hv h1
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i h1 : Adj (mp M) v w hw : Β¬False ⊒ Β¬w ∈ MultiPart.P M i
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
rw [mem_sdiff] at hw
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hw : w ∈ M.A \ MultiPart.P M i ⊒ Adj (mp M) v w
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hw : w ∈ M.A ∧ Β¬w ∈ MultiPart.P M i ⊒ Adj (mp M) v w
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
cases' hw with hA hni
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hw : w ∈ M.A ∧ Β¬w ∈ MultiPart.P M i ⊒ Adj (mp M) v w
case intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hA : w ∈ M.A hni : Β¬w ∈ MultiPart.P M i ⊒ Adj (mp M) v w
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
rw [M.uni] at hA
case intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hA : w ∈ M.A hni : Β¬w ∈ MultiPart.P M i ⊒ Adj (mp M) v w
case intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hA : w ∈ Finset.biUnion (range (M.t + 1)) fun i => MultiPart.P M i hni : Β¬w ∈ MultiPart.P M i ⊒ Adj (mp M) v w
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
rw [mem_biUnion] at hA
case intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hA : w ∈ Finset.biUnion (range (M.t + 1)) fun i => MultiPart.P M i hni : Β¬w ∈ MultiPart.P M i ⊒ Adj (mp M) v w
case intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hA : βˆƒ a, a ∈ range (M.t + 1) ∧ w ∈ MultiPart.P M a hni : Β¬w ∈ MultiPart.P M i ⊒ Adj (mp M) v w
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
obtain ⟨j, hj1, hj2⟩ := hA
case intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hA : βˆƒ a, a ∈ range (M.t + 1) ∧ w ∈ MultiPart.P M a hni : Β¬w ∈ MultiPart.P M i ⊒ Adj (mp M) v w
case intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hni : Β¬w ∈ MultiPart.P M i j : β„• hj1 : j ∈ range (M.t + 1) hj2 : w ∈ MultiPart.P M j ⊒ Adj (mp M) v w
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
refine' mp_imp_adj hi hj1 hv hj2 _
case intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hni : Β¬w ∈ MultiPart.P M i j : β„• hj1 : j ∈ range (M.t + 1) hj2 : w ∈ MultiPart.P M j ⊒ Adj (mp M) v w
case intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hni : Β¬w ∈ MultiPart.P M i j : β„• hj1 : j ∈ range (M.t + 1) hj2 : w ∈ MultiPart.P M j ⊒ i β‰  j
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
intro h
case intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hni : Β¬w ∈ MultiPart.P M i j : β„• hj1 : j ∈ range (M.t + 1) hj2 : w ∈ MultiPart.P M j ⊒ i β‰  j
case intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hni : Β¬w ∈ MultiPart.P M i j : β„• hj1 : j ∈ range (M.t + 1) hj2 : w ∈ MultiPart.P M j h : i = j ⊒ False
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
rw [h] at hni
case intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i hni : Β¬w ∈ MultiPart.P M i j : β„• hj1 : j ∈ range (M.t + 1) hj2 : w ∈ MultiPart.P M j h : i = j ⊒ False
case intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i j : β„• hni : Β¬w ∈ MultiPart.P M j hj1 : j ∈ range (M.t + 1) hj2 : w ∈ MultiPart.P M j h : i = j ⊒ False
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.nbhr_diff_parts
[99, 1]
[106, 77]
exact hni hj2
case intro.intro.intro Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v w : Ξ± M : MultiPart Ξ± hi : i ∈ range (M.t + 1) hv : v ∈ MultiPart.P M i j : β„• hni : Β¬w ∈ MultiPart.P M j hj1 : j ∈ range (M.t + 1) hj2 : w ∈ MultiPart.P M j h : i = j ⊒ False
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
ext
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i ⊒ neighborFinset (mp M) v = M.A \ MultiPart.P M i
case a Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ a✝ ∈ neighborFinset (mp M) v ↔ a✝ ∈ M.A \ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
constructor
case a Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ a✝ ∈ neighborFinset (mp M) v ↔ a✝ ∈ M.A \ MultiPart.P M i
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ a✝ ∈ neighborFinset (mp M) v β†’ a✝ ∈ M.A \ MultiPart.P M i case a.mpr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t ...
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
rw [mem_neighborFinset]
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ a✝ ∈ neighborFinset (mp M) v β†’ a✝ ∈ M.A \ MultiPart.P M i
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ Adj (mp M) v a✝ β†’ a✝ ∈ M.A \ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
intro h
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ Adj (mp M) v a✝ β†’ a✝ ∈ M.A \ MultiPart.P M i
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± h : Adj (mp M) v a✝ ⊒ a✝ ∈ M.A \ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
rw [adj_comm] at h
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± h : Adj (mp M) v a✝ ⊒ a✝ ∈ M.A \ MultiPart.P M i
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± h : Adj (mp M) a✝ v ⊒ a✝ ∈ M.A \ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
rw [mem_sdiff]
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± h : Adj (mp M) a✝ v ⊒ a✝ ∈ M.A \ MultiPart.P M i
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± h : Adj (mp M) a✝ v ⊒ a✝ ∈ M.A ∧ Β¬a✝ ∈ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
refine' ⟨nbhrs_imp h, _⟩
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± h : Adj (mp M) a✝ v ⊒ a✝ ∈ M.A ∧ Β¬a✝ ∈ MultiPart.P M i
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± h : Adj (mp M) a✝ v ⊒ Β¬a✝ ∈ MultiPart.P M i
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
exact not_nbhr_same_part hv.1 hv.2 h.symm
case a.mp Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± h : Adj (mp M) a✝ v ⊒ Β¬a✝ ∈ MultiPart.P M i
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
rw [mem_neighborFinset]
case a.mpr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ a✝ ∈ M.A \ MultiPart.P M i β†’ a✝ ∈ neighborFinset (mp M) v
case a.mpr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ a✝ ∈ M.A \ MultiPart.P M i β†’ Adj (mp M) v a✝
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_nbhd
[109, 1]
[114, 61]
exact nbhr_diff_parts hv.1 hv.2
case a.mpr Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i a✝ : Ξ± ⊒ a✝ ∈ M.A \ MultiPart.P M i β†’ Adj (mp M) v a✝
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg
[121, 1]
[122, 76]
rw [degree]
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i ⊒ degree (mp M) v = card (M.A \ MultiPart.P M i)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i ⊒ card (neighborFinset (mp M) v) = card (M.A \ MultiPart.P M i)
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg
[121, 1]
[122, 76]
rw [mp_nbhd hv]
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i ⊒ card (neighborFinset (mp M) v) = card (M.A \ MultiPart.P M i)
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_diff
[125, 1]
[126, 101]
rw [mp_deg hv]
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i ⊒ degree (mp M) v = card M.A - card (MultiPart.P M i)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i ⊒ card (M.A \ MultiPart.P M i) = card M.A - card (MultiPart.P M i)
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_diff
[125, 1]
[126, 101]
exact card_sdiff (sub_part hv.1)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± i : β„• v : Ξ± M : MultiPart Ξ± hv : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i ⊒ card (M.A \ MultiPart.P M i) = card M.A - card (MultiPart.P M i)
no goals
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_sum
[129, 1]
[135, 36]
nth_rw 1 [M.uni]
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± ⊒ βˆ‘ v in M.A, degree (mp M) v = βˆ‘ i in range (M.t + 1), card (MultiPart.P M i) * card (M.A \ MultiPart.P M i)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± ⊒ βˆ‘ v in Finset.biUnion (range (M.t + 1)) fun i => MultiPart.P M i, degree (mp M) v = βˆ‘ i in range (M.t + 1), card (MultiPart.P M i) * card (M.A \ MultiPart.P M i)
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_sum
[129, 1]
[135, 36]
rw [sum_biUnion (pair_disjoint M)]
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± ⊒ βˆ‘ v in Finset.biUnion (range (M.t + 1)) fun i => MultiPart.P M i, degree (mp M) v = βˆ‘ i in range (M.t + 1), card (MultiPart.P M i) * card (M.A \ MultiPart.P M i)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± ⊒ βˆ‘ x in range (M.t + 1), βˆ‘ i in MultiPart.P M x, degree (mp M) i = βˆ‘ i in range (M.t + 1), card (MultiPart.P M i) * card (M.A \ MultiPart.P M i)
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_sum
[129, 1]
[135, 36]
apply Finset.sum_congr rfl _
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± ⊒ βˆ‘ x in range (M.t + 1), βˆ‘ i in MultiPart.P M x, degree (mp M) i = βˆ‘ i in range (M.t + 1), card (MultiPart.P M i) * card (M.A \ MultiPart.P M i)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± ⊒ βˆ€ (x : β„•), x ∈ range (M.t + 1) β†’ βˆ‘ i in MultiPart.P M x, degree (mp M) i = card (MultiPart.P M x) * card (M.A \ MultiPart.P M x)
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_sum
[129, 1]
[135, 36]
intro x hx
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± ⊒ βˆ€ (x : β„•), x ∈ range (M.t + 1) β†’ βˆ‘ i in MultiPart.P M x, degree (mp M) i = card (MultiPart.P M x) * card (M.A \ MultiPart.P M x)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± x : β„• hx : x ∈ range (M.t + 1) ⊒ βˆ‘ i in MultiPart.P M x, degree (mp M) i = card (MultiPart.P M x) * card (M.A \ MultiPart.P M x)
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_sum
[129, 1]
[135, 36]
rw [Finset.card_eq_sum_ones, sum_mul, one_mul]
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± x : β„• hx : x ∈ range (M.t + 1) ⊒ βˆ‘ i in MultiPart.P M x, degree (mp M) i = card (MultiPart.P M x) * card (M.A \ MultiPart.P M x)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± x : β„• hx : x ∈ range (M.t + 1) ⊒ βˆ‘ i in MultiPart.P M x, degree (mp M) i = βˆ‘ x_1 in MultiPart.P M x, card (M.A \ MultiPart.P M x)
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_sum
[129, 1]
[135, 36]
apply Finset.sum_congr rfl _
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± x : β„• hx : x ∈ range (M.t + 1) ⊒ βˆ‘ i in MultiPart.P M x, degree (mp M) i = βˆ‘ x_1 in MultiPart.P M x, card (M.A \ MultiPart.P M x)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± x : β„• hx : x ∈ range (M.t + 1) ⊒ βˆ€ (x_1 : Ξ±), x_1 ∈ MultiPart.P M x β†’ degree (mp M) x_1 = card (M.A \ MultiPart.P M x)
https://github.com/jt496/Turan_4.git
329b6acff8f9b8f41609e3e5758ed80c61047eb5
Turan4/Multipartite.lean
SimpleGraph.mp_deg_sum
[129, 1]
[135, 36]
intro v hv
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± x : β„• hx : x ∈ range (M.t + 1) ⊒ βˆ€ (x_1 : Ξ±), x_1 ∈ MultiPart.P M x β†’ degree (mp M) x_1 = card (M.A \ MultiPart.P M x)
Ξ± : Type u_1 inst✝¹ : Fintype Ξ± inst✝ : DecidableEq Ξ± M : MultiPart Ξ± x : β„• hx : x ∈ range (M.t + 1) v : Ξ± hv : v ∈ MultiPart.P M x ⊒ degree (mp M) v = card (M.A \ MultiPart.P M x)