Expression of type Conditional

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, i, m, n
from proveit.core_expr_types import a_i, b_i, lambda_i
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import InSet
from proveit.numbers import Interval, Min, one

# build up the expression from sub-expressions
expr = Conditional(ScalarMult(lambda_i, TensorProd(a_i, b_i)), InSet(i, Interval(one, Min(m, n))))

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\{\lambda_{i} \cdot \left(a_{i} {\otimes} b_{i}\right) \textrm{ if } i \in \{1~\ldotp \ldotp~{\rm Min}\left(m, n\right)\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	24, 9
7	IndexedVar	variable: 10 index: 24
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	Variable
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	IndexedVar	variable: 19 index: 24
16	IndexedVar	variable: 20 index: 24
17	Literal
18	Operation	operator: 22 operands: 23
19	Variable
20	Variable
21	ExprTuple	24
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable