Expression of type ExprTuple

from the theory of proveit.linear_algebra.inner_products

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 B, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, i, lambda_, m, n, v
from proveit.core_expr_types import a_i, b_1_to_n, b_i, lambda_i
from proveit.linear_algebra import OrthoNormBases, ScalarMult, TensorProd, VecSum
from proveit.logic import Equals, Exists, InSet, Set
from proveit.numbers import Interval, Min, RealNonNeg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Min(m, n)
expr = ExprTuple(Lambda([b_1_to_n], Conditional(Exists(instance_param_or_params = [ExprRange(sub_expr1, IndexedVar(lambda_, sub_expr1), one, sub_expr2)], instance_expr = Equals(v, VecSum(index_or_indices = [i], summand = ScalarMult(lambda_i, TensorProd(a_i, b_i)), domain = Interval(one, sub_expr2))), domain = RealNonNeg).with_wrapping(), InSet(Set(b_1_to_n), OrthoNormBases(B)))))

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(b_{1}, b_{2}, \ldots, b_{n}\right) \mapsto \left\{\begin{array}{l}\exists_{\lambda_{1}, \lambda_{2}, \ldots, \lambda_{{\rm Min}\left(m, n\right)} \in \mathbb{R}^{\ge 0}}~\\
\left(v = \left(\sum_{i=1}^{{\rm Min}\left(m, n\right)} \left(\lambda_{i} \cdot \left(a_{i} {\otimes} b_{i}\right)\right)\right)\right)\end{array} \textrm{ if } \left\{b_{1}, b_{2}, \ldots, b_{n}\right\} \in \textrm{O.N.Bases}\left(B\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: 14 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 45 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operand: 21
11	ExprTuple	17
12	Conditional	value: 18 condition: 19
13	Literal
14	ExprTuple	20
15	Literal
16	ExprTuple	21
17	ExprRange	lambda_map: 22 start_index: 59 end_index: 60
18	Operation	operator: 23 operands: 24
19	Operation	operator: 25 operands: 26
20	ExprRange	lambda_map: 27 start_index: 59 end_index: 68
21	Variable
22	Lambda	parameter: 51 body: 41
23	Literal
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	30
27	Lambda	parameter: 51 body: 31
28	Variable
29	Operation	operator: 32 operand: 35
30	ExprRange	lambda_map: 34 start_index: 59 end_index: 60
31	IndexedVar	variable: 62 index: 51
32	Literal
33	ExprTuple	35
34	Lambda	parameter: 51 body: 36
35	Lambda	parameter: 66 body: 37
36	Operation	operator: 45 operands: 38
37	Conditional	value: 39 condition: 40
38	ExprTuple	41, 42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 45 operands: 46
41	IndexedVar	variable: 52 index: 51
42	Literal
43	Literal
44	ExprTuple	48, 49
45	Literal
46	ExprTuple	66, 50
47	ExprTuple	51
48	IndexedVar	variable: 52 index: 66
49	Operation	operator: 53 operands: 54
50	Operation	operator: 55 operands: 56
51	Variable
52	Variable
53	Literal
54	ExprTuple	57, 58
55	Literal
56	ExprTuple	59, 60
57	IndexedVar	variable: 61 index: 66
58	IndexedVar	variable: 62 index: 66
59	Literal
60	Operation	operator: 64 operands: 65
61	Variable
62	Variable
63	ExprTuple	66
64	Literal
65	ExprTuple	67, 68
66	Variable
67	Variable
68	Variable