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, b, 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, Forall, InSet
from proveit.numbers import Add, Complex, Mult, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k], instance_expr = 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), domain = Complex).with_wrapping(), And(InSet(i, Natural), InSet(j, Natural), InSet(k, Natural)))

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}{l}\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k} \in \mathbb{C}}~\\
\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}\right)\end{array} \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\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 operand: 6
2	Operation	operator: 20 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 10 body: 11
7	Operation	operator: 42 operands: 12
8	Operation	operator: 42 operands: 13
9	Operation	operator: 42 operands: 14
10	ExprTuple	52, 44, 54
11	Conditional	value: 15 condition: 16
12	ExprTuple	56, 17
13	ExprTuple	48, 17
14	ExprTuple	61, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	Operation	operator: 49 operands: 27
23	Operation	operator: 37 operands: 28
24	ExprRange	lambda_map: 29 start_index: 60 end_index: 56
25	ExprRange	lambda_map: 30 start_index: 60 end_index: 48
26	ExprRange	lambda_map: 31 start_index: 60 end_index: 61
27	ExprTuple	52, 32, 54
28	ExprTuple	33
29	Lambda	parameter: 68 body: 34
30	Lambda	parameter: 68 body: 35
31	Lambda	parameter: 68 body: 36
32	Operation	operator: 37 operands: 38
33	ExprRange	lambda_map: 39 start_index: 60 end_index: 48
34	Operation	operator: 42 operands: 40
35	Operation	operator: 42 operands: 41
36	Operation	operator: 42 operands: 43
37	Literal
38	ExprTuple	44
39	Lambda	parameter: 63 body: 45
40	ExprTuple	62, 46
41	ExprTuple	51, 46
42	Literal
43	ExprTuple	64, 46
44	ExprRange	lambda_map: 47 start_index: 60 end_index: 48
45	Operation	operator: 49 operands: 50
46	Literal
47	Lambda	parameter: 68 body: 51
48	Variable
49	Literal
50	ExprTuple	52, 53, 54
51	IndexedVar	variable: 57 index: 68
52	ExprRange	lambda_map: 55 start_index: 60 end_index: 56
53	IndexedVar	variable: 57 index: 63
54	ExprRange	lambda_map: 59 start_index: 60 end_index: 61
55	Lambda	parameter: 68 body: 62
56	Variable
57	Variable
58	ExprTuple	63
59	Lambda	parameter: 68 body: 64
60	Literal
61	Variable
62	IndexedVar	variable: 65 index: 68
63	Variable
64	IndexedVar	variable: 66 index: 68
65	Variable
66	Variable
67	ExprTuple	68
68	Variable