Expression of type Lambda

from the theory of proveit.linear_algebra.tensors

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, IndexedVar, Lambda, U, V, Variable, W, a, alpha, b, c, i, k
from proveit.core_expr_types import a_1_to_i, c_1_to_k
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import And, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i, b, c_1_to_k], Conditional(Equals(TensorProd(a_1_to_i, ScalarMult(alpha, b), c_1_to_k), ScalarMult(alpha, TensorProd(a_1_to_i, b, c_1_to_k))).with_wrapping_at(1), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), IndexedVar(U, sub_expr1)), one, i), InSet(b, V), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), IndexedVar(W, sub_expr1)), one, k))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(\alpha \cdot b\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \\  = \left(\alpha \cdot \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right) \end{array} \end{array} \textrm{ if } \left(a_{1} \in U_{1}\right) ,  \left(a_{2} \in U_{2}\right) ,  \ldots ,  \left(a_{i} \in U_{i}\right) ,  b \in V, \left(c_{1} \in W_{1}\right) ,  \left(c_{2} \in W_{2}\right) ,  \ldots ,  \left(c_{k} \in W_{k}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 26 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 25 operands: 13
9	Operation	operator: 23 operands: 14
10	ExprRange	lambda_map: 15 start_index: 39 end_index: 37
11	Operation	operator: 28 operands: 16
12	ExprRange	lambda_map: 17 start_index: 39 end_index: 40
13	ExprTuple	31, 18, 33
14	ExprTuple	30, 19
15	Lambda	parameter: 48 body: 20
16	ExprTuple	32, 21
17	Lambda	parameter: 48 body: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 25 operands: 26
20	Operation	operator: 28 operands: 27
21	Variable
22	Operation	operator: 28 operands: 29
23	Literal
24	ExprTuple	30, 32
25	Literal
26	ExprTuple	31, 32, 33
27	ExprTuple	43, 34
28	Literal
29	ExprTuple	44, 35
30	Variable
31	ExprRange	lambda_map: 36 start_index: 39 end_index: 37
32	Variable
33	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
34	IndexedVar	variable: 41 index: 48
35	IndexedVar	variable: 42 index: 48
36	Lambda	parameter: 48 body: 43
37	Variable
38	Lambda	parameter: 48 body: 44
39	Literal
40	Variable
41	Variable
42	Variable
43	IndexedVar	variable: 45 index: 48
44	IndexedVar	variable: 46 index: 48
45	Variable
46	Variable
47	ExprTuple	48
48	Variable