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, IndexedVar, Lambda, Variable, a, b, c, i, j, 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 Add, Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i, b_1_to_j, c_1_to_k], Conditional(Equals(Mult(a_1_to_i, Add(b_1_to_j), c_1_to_k), Add(ExprRange(sub_expr1, Mult(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j))).with_wrapping_at(2), And(ExprRange(sub_expr2, InSet(IndexedVar(a, sub_expr2), Complex), one, i), ExprRange(sub_expr2, InSet(IndexedVar(b, sub_expr2), Complex), one, j), ExprRange(sub_expr2, InSet(IndexedVar(c, sub_expr2), 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}, b_{1}, b_{2}, \ldots, b_{j}, 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(b_{1} +  b_{2} +  \ldots +  b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{1}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{2}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \ldots +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{j}\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(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{j} \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	39, 31, 41
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, 13
9	Operation	operator: 36 operands: 14
10	Operation	operator: 24 operands: 15
11	ExprRange	lambda_map: 16 start_index: 47 end_index: 43
12	ExprRange	lambda_map: 17 start_index: 47 end_index: 35
13	ExprRange	lambda_map: 18 start_index: 47 end_index: 48
14	ExprTuple	39, 19, 41
15	ExprTuple	20
16	Lambda	parameter: 55 body: 21
17	Lambda	parameter: 55 body: 22
18	Lambda	parameter: 55 body: 23
19	Operation	operator: 24 operands: 25
20	ExprRange	lambda_map: 26 start_index: 47 end_index: 35
21	Operation	operator: 29 operands: 27
22	Operation	operator: 29 operands: 28
23	Operation	operator: 29 operands: 30
24	Literal
25	ExprTuple	31
26	Lambda	parameter: 50 body: 32
27	ExprTuple	49, 33
28	ExprTuple	38, 33
29	Literal
30	ExprTuple	51, 33
31	ExprRange	lambda_map: 34 start_index: 47 end_index: 35
32	Operation	operator: 36 operands: 37
33	Literal
34	Lambda	parameter: 55 body: 38
35	Variable
36	Literal
37	ExprTuple	39, 40, 41
38	IndexedVar	variable: 44 index: 55
39	ExprRange	lambda_map: 42 start_index: 47 end_index: 43
40	IndexedVar	variable: 44 index: 50
41	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
42	Lambda	parameter: 55 body: 49
43	Variable
44	Variable
45	ExprTuple	50
46	Lambda	parameter: 55 body: 51
47	Literal
48	Variable
49	IndexedVar	variable: 52 index: 55
50	Variable
51	IndexedVar	variable: 53 index: 55
52	Variable
53	Variable
54	ExprTuple	55
55	Variable