Commit dbf0edb5 by Dennis Müller

### update

parent 824ec60b
 ... ... @@ -73,7 +73,7 @@ theory QuasiGroup : base:?Logic = theory CancellativeMagma : base:?Logic = include ?Magma ❙ /T MiKo: use this to make a view into quasisgroup Theory: they are cancellative❚ /T MiKo: use this to make a view into quasisgroup Theory: they are cancellative ❙ theory cancellativemagma_theory : base:?Logic = include ?Magma/magma_theory ❙ axiom_leftCancellative : ⊦ prop_leftCancellative op ❙ ... ...
 ... ... @@ -27,7 +27,7 @@ theory Module : base:?Logic = axiom_unit_scalars : ⊦ prop_unit_scalars scalarmult (scalars.rone) ❙ ❚ module = [R : ring] Mod `?Module/module_theory , R ❙ module = [R : ring] Mod `?Module/module_theory R ❙ distributive_right : {R : ring} ⊦ prop_dist2 (R.rtimes) (R.rplus) (R.rplus) ❘ # distributive_right 1 ❙ ... ... @@ -68,7 +68,7 @@ theory Vectorspace : base:?Logic = include ?Module/module_theory (scalars) ❙ bminus : U ⟶ U ⟶ U ❘ = [a,b] op a (inverse b) ❘ # 1 - 2❙ ❚ vectorspace : field ⟶ kind ❘ = [F : field] Mod `?Vectorspace/vectorspace_theory , F ❙ vectorspace : field ⟶ kind ❘ = [F : field] Mod `?Vectorspace/vectorspace_theory F ❙ include ?Module ❙ ... ... @@ -160,6 +160,6 @@ theory LinearMaps : base:?Logic = .. ❙ ❚ linearMap : field ⟶ ℕ+ ⟶ ℕ+ ⟶ type ❘ = [K : field][n1 : ℕ+,n2 : ℕ+] Mod `?LinearMaps/linearMap_theory , K , n1 , n2 ❘ # linearMap 1 2 3❙ linearMap : field ⟶ ℕ+ ⟶ ℕ+ ⟶ type ❘ = [K : field][n1 : ℕ+,n2 : ℕ+] Mod `?LinearMaps/linearMap_theory K n1 n2 ❘ # linearMap 1 2 3❙ // L : linearMap realfield 2 3 ❙ ❚
 ... ... @@ -6,7 +6,7 @@ import arith http://mathhub.info/MitM/smglom/arithmetics ❚ theory FinSequences : base:?Logic = include arith:?NaturalArithmetics ❙ below : ℕ ⟶ type ❙ below : ℕ ⟶ type ❘ = [n] ⟨ x : ℕ | ⊦ x < n ⟩ ❙ toBelow : {n : ℕ} below (Succ n) ❘# toB 1❙ succBelow : {n : ℕ} below n ⟶ below (Succ n) ❘# succB 2❙ ... ... @@ -38,5 +38,5 @@ theory FinSequences : base:?Logic = belowShift : {n : ℕ , m : ℕ} below n ⟶ below (n + m)❙ // belowShift_base : {n, b} ⊦ belowShift n 0 b ≐ b❙ // finSeqSum : {n : ℕ , b : below n} // finSeqSum : {n : ℕ , b : below n} ❙ ❚
 ... ... @@ -32,7 +32,7 @@ theory Partition : base:?Logic = axiom_nonEmpty : ⊦ ¬ (∅ ∈ coll) ❙ axiom_pairwisedisjoint : ⊦ pairwiseDisjoint coll ❙ ❚ partition = [X : type] Mod `?Partition/partition_theory , X ❙ partition = [X : type] Mod `?Partition/partition_theory (X) ❙ ❚ // theory TaggedPartition : base:?Logic = ... ...
 ... ... @@ -38,7 +38,7 @@ theory Measure : base:?Logic = axiom_emptyiszero : ⊦ μ (elem (A.coll) ∅ ) ≐ 0 ❙ axiom_sigmaadditivity : ⊦ prop_sigmaAdditive (A.coll) measure ❙ ❚ measure = [X : type, A : sigmaAlgebra X] Mod `?Measure/measure_theory , X , A ❙ measure = [X : type, A : sigmaAlgebra X] Mod `?Measure/measure_theory X A ❙ measureSpace = {' universe : type , sigma_algebra : sigmaAlgebra universe , ... ...
 ... ... @@ -21,7 +21,7 @@ theory SetAlgebra : base:?Logic = lemma_finiteUnion : ⊦ prop_finiteUnion coll ❘ = sketch "by de Morgan" ❙ lemma_empty : ⊦ prop_emptyInColl coll ❘ = sketch "\$∅\$ is the complement of \$X\$" ❙ ❚ setAlgebra = [X : type] Mod `?SetAlgebra/setAlgebra_theory , X ❙ setAlgebra = [X : type] Mod `?SetAlgebra/setAlgebra_theory X ❙ ❚ theory SigmaAlgebra : base:?Logic = ... ... @@ -45,7 +45,7 @@ theory SigmaAlgebra : base:?Logic = ❚ ❚ sigmaAlgebra = [X : type] Mod `?SigmaAlgebra/sigmaAlgebra_theory , X ❙ sigmaAlgebra = [X : type] Mod `?SigmaAlgebra/sigmaAlgebra_theory X ❙ ❚ theory Measurable : base:?Logic = ... ...
 ... ... @@ -159,7 +159,7 @@ theory SetCollection : base:?Logic = coll : collection X ❙ colltype = setastype coll ❙ ❚ setColl = [X : type] Mod `?SetCollection/setColl_theory , X ❙ setColl = [X : type] Mod `?SetCollection/setColl_theory (X) ❙ emptySetInType : {T, S : setColl T, emptyincoll : ⊦ ∅ ∈ (S.coll) } S.colltype ❘ # ∅t %I1 %I2 %I3 ❙ fullSetInType : {T, S : setColl T, fullincoll : ⊦ (fullset T) ∈ (S.coll) } S.colltype ❘ # fullt %I1 %I2 %I3 ❙ ... ...
 ... ... @@ -17,7 +17,7 @@ theory OpenSetTopology : base:?Logic = axiom_intersection: ⊦ prop_finiteIntersection coll ❙ ❚ topology = [X : type] Mod `?OpenSetTopology/topology_theory , X❙ topology = [X : type] Mod `?OpenSetTopology/topology_theory (X)❙ topologicalSpace : kind ❘ = {' universe : type , topology : topology universe ... ... @@ -136,7 +136,7 @@ theory HausdorffTopology : base:?Logic = include ?OpenSetTopology/topology_theory (X) ❙ ishausdorff : ⊦ hausdorffProperty X coll ❙ ❚ hausdorffTopology : type ⟶ type ❘ = [X : type] Mod `?HausdorffTopology/hausdorff_theory , X ❙ hausdorffTopology : type ⟶ type ❘ = [X : type] Mod `?HausdorffTopology/hausdorff_theory (X) ❙ hausdorffSpace : kind ❘= {' universe : type , ... ...
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