Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda(n, 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(n \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 44 body: 3
2	ExprTuple	44
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 37 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	44, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	39, 48
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23
19	Operation	operator: 45 operands: 24
20	Operation	operator: 34 operands: 25
21	ExprRange	lambda_map: 26 start_index: 43 end_index: 44
22	Operation	operator: 37 operands: 27
23	Operation	operator: 28 operands: 29
24	ExprTuple	30, 48
25	ExprTuple	31
26	Lambda	parameter: 51 body: 32
27	ExprTuple	48, 41
28	Literal
29	ExprTuple	48, 33
30	Operation	operator: 34 operands: 35
31	ExprRange	lambda_map: 36 start_index: 43 end_index: 44
32	Operation	operator: 37 operands: 38
33	Literal
34	Literal
35	ExprTuple	39
36	Lambda	parameter: 51 body: 40
37	Literal
38	ExprTuple	47, 41
39	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
40	Operation	operator: 45 operands: 46
41	Literal
42	Lambda	parameter: 51 body: 47
43	Literal
44	Variable
45	Literal
46	ExprTuple	47, 48
47	IndexedVar	variable: 49 index: 51
48	Variable
49	Variable
50	ExprTuple	51
51	Variable