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 Equals, Forall, InSet, NotEquals
from proveit.numbers import Add, Complex, NaturalPos, frac, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [x_1_to_n, y], instance_expr = Equals(frac(Add(x_1_to_n), y), Add(ExprRange(sub_expr1, frac(IndexedVar(x, sub_expr1), y), one, n))), domain = Complex, condition = NotEquals(y, zero)), InSet(n, NaturalPos))

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_{x_{1}, x_{2}, \ldots, x_{n}, y \in \mathbb{C}~|~y \neq 0}~\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)\right) \textrm{ if } n \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: 34 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	41, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	36, 45
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19, 20
16	Operation	operator: 42 operands: 21
17	Operation	operator: 31 operands: 22
18	ExprRange	lambda_map: 23 start_index: 40 end_index: 41
19	Operation	operator: 34 operands: 24
20	Operation	operator: 25 operands: 26
21	ExprTuple	27, 45
22	ExprTuple	28
23	Lambda	parameter: 48 body: 29
24	ExprTuple	45, 38
25	Literal
26	ExprTuple	45, 30
27	Operation	operator: 31 operands: 32
28	ExprRange	lambda_map: 33 start_index: 40 end_index: 41
29	Operation	operator: 34 operands: 35
30	Literal
31	Literal
32	ExprTuple	36
33	Lambda	parameter: 48 body: 37
34	Literal
35	ExprTuple	44, 38
36	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
37	Operation	operator: 42 operands: 43
38	Literal
39	Lambda	parameter: 48 body: 44
40	Literal
41	Variable
42	Literal
43	ExprTuple	44, 45
44	IndexedVar	variable: 46 index: 48
45	Variable
46	Variable
47	ExprTuple	48
48	Variable