Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 27 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 26 operands: 14
10	Operation	operator: 24 operands: 15
11	ExprRange	lambda_map: 16 start_index: 40 end_index: 38
12	Operation	operator: 29 operands: 17
13	ExprRange	lambda_map: 18 start_index: 40 end_index: 41
14	ExprTuple	32, 19, 34
15	ExprTuple	31, 20
16	Lambda	parameter: 49 body: 21
17	ExprTuple	33, 22
18	Lambda	parameter: 49 body: 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 26 operands: 27
21	Operation	operator: 29 operands: 28
22	Variable
23	Operation	operator: 29 operands: 30
24	Literal
25	ExprTuple	31, 33
26	Literal
27	ExprTuple	32, 33, 34
28	ExprTuple	44, 35
29	Literal
30	ExprTuple	45, 36
31	Variable
32	ExprRange	lambda_map: 37 start_index: 40 end_index: 38
33	Variable
34	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
35	IndexedVar	variable: 42 index: 49
36	IndexedVar	variable: 43 index: 49
37	Lambda	parameter: 49 body: 44
38	Variable
39	Lambda	parameter: 49 body: 45
40	Literal
41	Variable
42	Variable
43	Variable
44	IndexedVar	variable: 46 index: 49
45	IndexedVar	variable: 47 index: 49
46	Variable
47	Variable
48	ExprTuple	49
49	Variable