### finally doing more probability

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 ... ... @@ -6,3 +6,4 @@ Declares http://mathhub.info/MitM/smglom/arithmetics/naturals.omdoc http://mathh Declares http://mathhub.info/MitM/smglom/arithmetics/naturals.omdoc http://mathhub.info/MitM/smglom/arithmetics?Between Declares http://mathhub.info/MitM/smglom/arithmetics/naturals.omdoc http://mathhub.info/MitM/smglom/arithmetics?NatConversions Declares http://mathhub.info/MitM/smglom/arithmetics/naturals.omdoc http://mathhub.info/MitM/smglom/arithmetics?INatProps Declares http://mathhub.info/MitM/smglom/arithmetics/naturals.omdoc http://mathhub.info/MitM/smglom/arithmetics?CompDec
 ... ... @@ -2,3 +2,4 @@ document http://mathhub.info/MitM/smglom/arithmetics/reals.omdoc Declares http://mathhub.info/MitM/smglom/arithmetics/reals.omdoc http://mathhub.info/MitM/smglom/arithmetics?RealNumbers Declares http://mathhub.info/MitM/smglom/arithmetics/reals.omdoc http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics Declares http://mathhub.info/MitM/smglom/arithmetics/reals.omdoc http://mathhub.info/MitM/smglom/arithmetics?ExtendedReals Declares http://mathhub.info/MitM/smglom/arithmetics/reals.omdoc http://mathhub.info/MitM/smglom/arithmetics?RealProperties
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 datatypeconstructor http://mathhub.info/MitM/smglom/calculus?Intervals?interval dataconstructor http://mathhub.info/MitM/smglom/calculus?Intervals?closedInterval datatypeconstructor http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci datatypeconstructor http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci_alt datatypeconstructor http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi theory http://mathhub.info/MitM/smglom/calculus?Intervals HasMeta http://mathhub.info/MitM/smglom/calculus?Intervals http://mathhub.info/MitM/Foundation?Logic Includes http://mathhub.info/MitM/smglom/calculus?Intervals http://mathhub.info/MitM/Foundation?RealLiterals ... ... @@ -102,3 +104,18 @@ DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci?definition DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci?definition http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics?leq?type DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci?definition http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci?definition http://mathhub.info/MitM/Foundation?Logic?and?type Declares http://mathhub.info/MitM/smglom/calculus?Intervals http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci_alt constant http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci_alt DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci_alt?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci_alt?definition http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics?predAsSub?type DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci_alt?definition http://mathhub.info/MitM/Foundation?Logic?prop?definition DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci_alt?definition http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics?leq?type DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci_alt?definition http://mathhub.info/MitM/Foundation?Logic?and?type Declares http://mathhub.info/MitM/smglom/calculus?Intervals http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi constant http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi?definition http://mathhub.info/MitM/Foundation?Logic?ded?type DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi?definition http://mathhub.info/MitM/Foundation?Logic?prop?definition DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi?definition http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics?leq?type DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi?definition http://mathhub.info/MitM/Foundation?Logic?ded?definition DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi?definition http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci?type DependsOn http://mathhub.info/MitM/smglom/calculus?Intervals?ascendingCi?definition http://mathhub.info/MitM/smglom/calculus?Intervals?type_ci?definition
scratch.mmt 0 → 100644
 namespace http://mathhub.info/MitM/smglom ❚ import base http://mathhub.info/MitM/Foundation ❚ import lfxdat http://gl.mathhub.info/MMT/LFX/Datatypes❚ theory scratch : base:?Logic = include http://gl.mathhub.info/MMT/LFX/Datatypes?LFLists ❙ include http://mathhub.info/MitM/smglom/arithmetics?NaturalArithmetics ❙ subst : {A : type}{a : A} {b : A} {P : A ⟶ type} ⊦ a ≐ b ⟶ P a ⟶ P b ❙ x : ℕ ❙ n : ℕ ❙ y : ℕ ❙ hh : ⊦ x < n ❙ hhh : ⊦ x ≐ y ❙ test : ⊦ y < n ❘= subst ℕ x y ([v] ⊦ v < n) hhh hh ❙ ❚
 namespace http://mathhub.info/MitM/smglom/Datatypes ❚ import base http://mathhub.info/MitM/Foundation ❚ import arith http://mathhub.info/MitM/smglom/arithmetics ❚ theory List : base:?Logic = list : type ⟶ type ❙ cons : {A : type} A ⟶ list A ⟶ list A ❙ nil : {A : type } list A ❙ ❚ theory ListFunctions : base:?Logic = include http://mathhub.info/MitM/smglom/Datatypes?List ❙ include http://mathhub.info/MitM/smglom/arithmetics?NaturalArithmetics ❙ length : {A : type} list A ⟶ ℕ ❙ lenghtB : {A : type} ⊦ length A (nil A) ≐ 0 ❙ lengthS : {A : type}{a : A}{ls : list A} ⊦ length A (cons A a ls) ≐ Succ (length A ls)❙ lemma_succ_cons : {A : type}{n : ℕ} {a : A}{ls : list A} ⊦ ((Succ n) < length A (cons A a ls)) ⟶ ⊦ n < length A ls ❘# lemma_succ_cons 1 2 3 4 5 ❙ listAt : {A : type}{n : ℕ }{ls : list A} ⊦ n < length A ls ⟶ A ❙ listAtB : {A : type } {a : A} {ls : list A}{h : ⊦ 0 < length A (cons A a ls)} ⊦ listAt A 0 (cons A a ls) h ≐ a ❙ listAtS : {A : type}{n : ℕ} {a : A} {ls : list A} {h : ⊦ (Succ n) < length A (cons A a ls)} ⊦ listAt A (Succ n) (cons A a ls) h ≐ listAt A n ls (lemma_succ_cons A n a ls h) ❙ ❚
 namespace http://mathhub.info/MitM/smglom/Datatypes ❚ import base http://mathhub.info/MitM/Foundation ❚ import arith http://mathhub.info/MitM/smglom/arithmetics ❚ theory vectorFunctions : base:?Logic = include http://mathhub.info/MitM/Foundation?Vectors ❙ include http://mathhub.info/MitM/smglom/arithmetics?NaturalArithmetics ❙ atVec : {A : type}{n : ℕ} {i : ℕ} vector A n ⟶ ⊦ i < n ⟶ A ❙ atVecB : {A : type} {n : ℕ} {a : A} {vs : vector A n}⊦ atVec A (Succ n) (0) (a ; vs) (lemma_zero_succ_lt n) ≐ a ❙ atVecS : {A : type} {n : ℕ} {i : ℕ} {a : A} {vs : vector A n} {h : ⊦ (Succ i) < (Succ n)}⊦ atVec A (Succ n) (Succ i) (a ; vs) h ≐ atVec A n i vs (lemma_succ_succ_lt i n h ) ❙ ❚
 ... ... @@ -80,6 +80,8 @@ theory NaturalArithmetics : base:?Logic = lemma_zero_succ_lt : {n : ℕ} ⊦ 0 < `?NaturalNumbers?succ n ❘# lemma_zero_succ_lt 1 ❙ lemma_lt_succ_succ : {a : ℕ} {b : ℕ} ⊦ a < b ⟶ ⊦ `?NaturalNumbers?succ a < `?NaturalNumbers?succ b ❘# lemma_lt_succ_succ 1 2 3 ❙ lemma_le_succ_succ : {a : ℕ} {b : ℕ} ⊦ a ≤ b ⟶ ⊦ `?NaturalNumbers?succ a ≤ `?NaturalNumbers?succ b ❘ # lemma_le_succ_succ 1 2 3 ❙ lemma_succ_succ_lt : {a : ℕ} {b : ℕ} ⊦ (Succ a) < (Succ b) ⟶ ⊦ a < b ❘ # lemma_succ_succ_lt 1 2 3❙ lemma_succ_succ_le : {a : ℕ} {b : ℕ} ⊦ (Succ a) ≤ (Succ b) ⟶ ⊦ a ≤ b ❘ # lemma_succ_succ_le 1 2 3❙ // added by sw ❙ ... ...
 ... ... @@ -92,3 +92,10 @@ theory ExtendedReals : base:?Logic = // leq : ℝ∞ ⟶ ℝ∞ ⟶ bool ❘ # 1 ≤ 2 prec 101 ❙ // TODO neginfty : ℝ∞ ❘ = - ∞ ❘ # -∞ ❙ ❚ theory RealProperties : base:?Logic = include ?ExtendedReals ❙ is_rat : ℝ ⟶ bool ❘ = [r] ∃ [n] ∃ [d] r ≐ fraction n d ❙ ❚ \ No newline at end of file
 ... ... @@ -52,6 +52,9 @@ theory Intervals : base:?Logic = rightPred : ℝ ⟶ ℝ ⟶ prop := ([x,y] x ≤ y) , predicate : ℝ ⟶ prop := [x] leftPred left x ∧ rightPred x right , tp : type := pred predicate'} ❙ ascendingCi : type ❘ = ⟨ x :type_ci | ⊦ (x.left) ≤ (x.right) ⟩ ❙ ❚ theory OneCuboid : base:?Logic = ... ...
 ... ... @@ -29,10 +29,17 @@ theory SigmaOperatorTheorems : base:?Logic = theory BorelExample : base:?Logic = include base:?Vectors ❙ include arith:?NaturalNumbers ❙ include arith:?RealProperties ❙ include http://mathhub.info/MitM/smglom/calculus?Intervals ❙ include http://mathhub.info/MitM/smglom/Datatypes?ListFunctions ❙ n : ℕ ❙ // vspace = finite_vectorspace realfield n ❙ // this line crashes intellij ❙ Ω = vector ℝ n❙ ndimQuardRat = ⟨ vector ℝ n | ⟩ ❙ vectorInIntervals : vector ℝ n ⟶ {lss : list ascendingCi} ⊦ (n ≐ length ascendingCi lss) ⟶ bool ❘ = [v , lss , h ] ∀ [x : ℕ ] ∀ [h : ⊦ x < n] listAt ascendingCi x (subst ) ≤ atVec ℝ n x v h ❙ // ndimQuardRat = [ls : list ]⟨ vector ℝ n | ⟩ ❙ ❚
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