Expression of type Lambda

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, Lambda, 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 = Lambda(i, 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())

i \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 25 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	25, 10
8	IndexedVar	variable: 11 index: 25
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Variable
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19
16	IndexedVar	variable: 20 index: 25
17	IndexedVar	variable: 21 index: 25
18	Literal
19	Operation	operator: 23 operands: 24
20	Variable
21	Variable
22	ExprTuple	25
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Variable
27	Variable