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Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 591 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.32.0

Succ Succ Above comm

TensorSpecies.Tensor.IsReindexing.succSuccAbove_comm

Plain-language statement

Removing two pairs of entries from c in either order gives the same colour list: removing the i1-th and j1-th entries and then the (shifted) i2-th and j2-th entries matches removing the i2-th and j2-th entries first and then the (shifted) i1-th and j1-th entries, via the identity permutation. This is used for the commutation of two *cont...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Prod T assoc

TensorSpecies.Tensor.prodT_assoc

Project documentation

Rewriting basis for the product in terms of the tensor product basis. -/ lemma basis_prod_eq {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} : basis (S := S) (Fin.append c c1) = (((Tensor.basis (S := S) c).tensorProduct (Tensor.basis (S := S) c1)).reindex (ComponentIdx.prod.symm)).map tensorEquivProd := by ext b simp [ComponentIdx.prod, tensorEquivProd] rw [pr...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Prod T assoc

TensorSpecies.Tensor.prodT_assoc'

Project documentation

Rewriting basis for the product in terms of the tensor product basis. -/ lemma basis_prod_eq {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} : basis (S := S) (Fin.append c c1) = (((Tensor.basis (S := S) c).tensorProduct (Tensor.basis (S := S) c1)).reindex (ComponentIdx.prod.symm)).map tensorEquivProd := by ext b simp [ComponentIdx.prod, tensorEquivProd] rw [pr...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Prod T equivariant

TensorSpecies.Tensor.prodT_equivariant

Project documentation

Rewriting basis for the product in terms of the tensor product basis. -/ lemma basis_prod_eq {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} : basis (S := S) (Fin.append c c1) = (((Tensor.basis (S := S) c).tensorProduct (Tensor.basis (S := S) c1)).reindex (ComponentIdx.prod.symm)).map tensorEquivProd := by ext b simp [ComponentIdx.prod, tensorEquivProd] rw [pr...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Prod T perm T left

TensorSpecies.Tensor.prodT_permT_left

Project documentation

Rewriting basis for the product in terms of the tensor product basis. -/ lemma basis_prod_eq {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} : basis (S := S) (Fin.append c c1) = (((Tensor.basis (S := S) c).tensorProduct (Tensor.basis (S := S) c1)).reindex (ComponentIdx.prod.symm)).map tensorEquivProd := by ext b simp [ComponentIdx.prod, tensorEquivProd] rw [pr...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Prod T perm T right

TensorSpecies.Tensor.prodT_permT_right

Project documentation

Rewriting basis for the product in terms of the tensor product basis. -/ lemma basis_prod_eq {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} : basis (S := S) (Fin.append c c1) = (((Tensor.basis (S := S) c).tensorProduct (Tensor.basis (S := S) c1)).reindex (ComponentIdx.prod.symm)).map tensorEquivProd := by ext b simp [ComponentIdx.prod, tensorEquivProd] rw [pr...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record