Expression of type Lambda

from the theory of proveit.numbers.multiplication

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, Function, IndexedVar, Lambda, Q, Variable, a, c, f, i, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, Sum, one
from proveit.numbers.summation import summation_b1toj_fQ

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [b_1_to_j]
expr = Lambda([a_1_to_i, c_1_to_k], Conditional(Equals(Mult(a_1_to_i, summation_b1toj_fQ, c_1_to_k), Sum(index_or_indices = sub_expr2, summand = Mult(a_1_to_i, Function(f, sub_expr2), c_1_to_k), condition = Function(Q, sub_expr2))).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Complex), 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(a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right)\right] \end{array} \end{array} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right), \left(c_{1} \in \mathbb{C}\right) ,  \left(c_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(c_{k} \in \mathbb{C}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	34, 36
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
9	Operation	operator: 31 operands: 13
10	Operation	operator: 21 operand: 18
11	ExprRange	lambda_map: 15 start_index: 49 end_index: 39
12	ExprRange	lambda_map: 16 start_index: 49 end_index: 43
13	ExprTuple	34, 17, 36
14	ExprTuple	18
15	Lambda	parameter: 55 body: 19
16	Lambda	parameter: 55 body: 20
17	Operation	operator: 21 operand: 27
18	Lambda	parameters: 41 body: 23
19	Operation	operator: 25 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	ExprTuple	27
23	Conditional	value: 28 condition: 33
24	ExprTuple	44, 29
25	Literal
26	ExprTuple	46, 29
27	Lambda	parameters: 41 body: 30
28	Operation	operator: 31 operands: 32
29	Literal
30	Conditional	value: 35 condition: 33
31	Literal
32	ExprTuple	34, 35, 36
33	Operation	operator: 37 operands: 41
34	ExprRange	lambda_map: 38 start_index: 49 end_index: 39
35	Operation	operator: 40 operands: 41
36	ExprRange	lambda_map: 42 start_index: 49 end_index: 43
37	Variable
38	Lambda	parameter: 55 body: 44
39	Variable
40	Variable
41	ExprTuple	45
42	Lambda	parameter: 55 body: 46
43	Variable
44	IndexedVar	variable: 47 index: 55
45	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
46	IndexedVar	variable: 51 index: 55
47	Variable
48	Lambda	parameter: 55 body: 52
49	Literal
50	Variable
51	Variable
52	IndexedVar	variable: 53 index: 55
53	Variable
54	ExprTuple	55
55	Variable