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 Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, i, lambda_, m, n, v
from proveit.core_expr_types import a_i, b_i, lambda_i
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import And, Equals, InSet
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 = IndexedVar(lambda_, sub_expr1)
sub_expr3 = Min(m, n)
expr = ExprTuple(Lambda([ExprRange(sub_expr1, sub_expr2, one, sub_expr3)], Conditional(Equals(v, VecSum(index_or_indices = [i], summand = ScalarMult(lambda_i, TensorProd(a_i, b_i)), domain = Interval(one, sub_expr3))), And(ExprRange(sub_expr1, InSet(sub_expr2, RealNonNeg), one, sub_expr3)))))

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(\lambda_{1}, \lambda_{2}, \ldots, \lambda_{{\rm Min}\left(m, n\right)}\right) \mapsto \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) \textrm{ if } \left(\lambda_{1} \in \mathbb{R}^{\ge 0}\right) \land  \left(\lambda_{2} \in \mathbb{R}^{\ge 0}\right) \land  \ldots \land  \left(\lambda_{{\rm Min}\left(m, n\right)} \in \mathbb{R}^{\ge 0}\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: 2 body: 3
2	ExprTuple	4
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 42 end_index: 43
5	Operation	operator: 8 operands: 9
6	Operation	operator: 10 operands: 11
7	Lambda	parameter: 34 body: 24
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14
12	Variable
13	Operation	operator: 15 operand: 18
14	ExprRange	lambda_map: 17 start_index: 42 end_index: 43
15	Literal
16	ExprTuple	18
17	Lambda	parameter: 34 body: 19
18	Lambda	parameter: 49 body: 20
19	Operation	operator: 28 operands: 21
20	Conditional	value: 22 condition: 23
21	ExprTuple	24, 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	IndexedVar	variable: 35 index: 34
25	Literal
26	Literal
27	ExprTuple	31, 32
28	Literal
29	ExprTuple	49, 33
30	ExprTuple	34
31	IndexedVar	variable: 35 index: 49
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operands: 39
34	Variable
35	Variable
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42, 43
40	IndexedVar	variable: 44 index: 49
41	IndexedVar	variable: 45 index: 49
42	Literal
43	Operation	operator: 47 operands: 48
44	Variable
45	Variable
46	ExprTuple	49
47	Literal
48	ExprTuple	50, 51
49	Variable
50	Variable
51	Variable