Expression of type Conditional

from the theory of proveit.numbers.division

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, n, x, y
from proveit.core_expr_types import x_1_to_n
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Complex, frac, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(x, sub_expr1)
expr = Conditional(Equals(frac(Add(x_1_to_n), y), Add(ExprRange(sub_expr1, frac(sub_expr2, y), one, n))), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, n), InSet(y, Complex), NotEquals(y, zero)))

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\{\frac{x_{1} +  x_{2} +  \ldots +  x_{n}}{y} = \left(\frac{x_{1}}{y} +  \frac{x_{2}}{y} +  \ldots +  \frac{x_{n}}{y}\right) \textrm{ if } \left(x_{1} \in \mathbb{C}\right) ,  \left(x_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(x_{n} \in \mathbb{C}\right) ,  y \in \mathbb{C} ,  y \neq 0\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: 33 operands: 12
8	Operation	operator: 22 operands: 13
9	ExprRange	lambda_map: 14 start_index: 31 end_index: 32
10	Operation	operator: 25 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18, 36
13	ExprTuple	19
14	Lambda	parameter: 39 body: 20
15	ExprTuple	36, 29
16	Literal
17	ExprTuple	36, 21
18	Operation	operator: 22 operands: 23
19	ExprRange	lambda_map: 24 start_index: 31 end_index: 32
20	Operation	operator: 25 operands: 26
21	Literal
22	Literal
23	ExprTuple	27
24	Lambda	parameter: 39 body: 28
25	Literal
26	ExprTuple	35, 29
27	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
28	Operation	operator: 33 operands: 34
29	Literal
30	Lambda	parameter: 39 body: 35
31	Literal
32	Variable
33	Literal
34	ExprTuple	35, 36
35	IndexedVar	variable: 37 index: 39
36	Variable
37	Variable
38	ExprTuple	39
39	Variable