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, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Mult(a_1_to_n, b), Mult(Mult(a_1_to_n), b)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, n), InSet(b, Complex)))

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\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n} \cdot b\right) = \left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \cdot b\right) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{n} \in \mathbb{C}\right) ,  b \in \mathbb{C}\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
7	Operation	operator: 18 operands: 11
8	Operation	operator: 18 operands: 12
9	ExprRange	lambda_map: 13 start_index: 25 end_index: 26
10	Operation	operator: 20 operands: 14
11	ExprTuple	22, 17
12	ExprTuple	15, 17
13	Lambda	parameter: 30 body: 16
14	ExprTuple	17, 23
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	27, 23
22	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
23	Literal
24	Lambda	parameter: 30 body: 27
25	Literal
26	Variable
27	IndexedVar	variable: 28 index: 30
28	Variable
29	ExprTuple	30
30	Variable