Expression of type Conditional

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, 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 = 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\{\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()

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	9, 10, 11
7	Operation	operator: 34 operands: 12
8	Operation	operator: 22 operands: 13
9	ExprRange	lambda_map: 14 start_index: 45 end_index: 41
10	ExprRange	lambda_map: 15 start_index: 45 end_index: 33
11	ExprRange	lambda_map: 16 start_index: 45 end_index: 46
12	ExprTuple	37, 17, 39
13	ExprTuple	18
14	Lambda	parameter: 53 body: 19
15	Lambda	parameter: 53 body: 20
16	Lambda	parameter: 53 body: 21
17	Operation	operator: 22 operands: 23
18	ExprRange	lambda_map: 24 start_index: 45 end_index: 33
19	Operation	operator: 27 operands: 25
20	Operation	operator: 27 operands: 26
21	Operation	operator: 27 operands: 28
22	Literal
23	ExprTuple	29
24	Lambda	parameter: 48 body: 30
25	ExprTuple	47, 31
26	ExprTuple	36, 31
27	Literal
28	ExprTuple	49, 31
29	ExprRange	lambda_map: 32 start_index: 45 end_index: 33
30	Operation	operator: 34 operands: 35
31	Literal
32	Lambda	parameter: 53 body: 36
33	Variable
34	Literal
35	ExprTuple	37, 38, 39
36	IndexedVar	variable: 42 index: 53
37	ExprRange	lambda_map: 40 start_index: 45 end_index: 41
38	IndexedVar	variable: 42 index: 48
39	ExprRange	lambda_map: 44 start_index: 45 end_index: 46
40	Lambda	parameter: 53 body: 47
41	Variable
42	Variable
43	ExprTuple	48
44	Lambda	parameter: 53 body: 49
45	Literal
46	Variable
47	IndexedVar	variable: 50 index: 53
48	Variable
49	IndexedVar	variable: 51 index: 53
50	Variable
51	Variable
52	ExprTuple	53
53	Variable