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, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import Add, Complex, Mult, Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Equals(Add(a_1_to_n), Mult(x, n)), domain = Set(x)), And(InSet(n, Natural), InSet(x, 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\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in \left\{x\right\}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{n}\right) = \left(x \cdot n\right)\right) \textrm{ if } n \in \mathbb{N} ,  x \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 operand: 6
2	Operation	operator: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 24 body: 9
7	Operation	operator: 33 operands: 10
8	Operation	operator: 33 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	32, 14
11	ExprTuple	42, 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	Literal
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprRange	lambda_map: 27 start_index: 31 end_index: 32
23	Literal
24	ExprTuple	28
25	Literal
26	ExprTuple	42, 32
27	Lambda	parameter: 41 body: 29
28	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
29	Operation	operator: 33 operands: 34
30	Lambda	parameter: 41 body: 35
31	Literal
32	Variable
33	Literal
34	ExprTuple	35, 36
35	IndexedVar	variable: 37 index: 41
36	Operation	operator: 39 operand: 42
37	Variable
38	ExprTuple	41
39	Literal
40	ExprTuple	42
41	Variable
42	Variable