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 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 = ExprTuple(Lambda([x_1_to_n, y], 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(\left(x_{1}, x_{2}, \ldots, x_{n}, y\right) \mapsto \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..\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	parameters: 2 body: 3
2	ExprTuple	30, 39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 36 operands: 15
11	Operation	operator: 25 operands: 16
12	ExprRange	lambda_map: 17 start_index: 34 end_index: 35
13	Operation	operator: 28 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21, 39
16	ExprTuple	22
17	Lambda	parameter: 42 body: 23
18	ExprTuple	39, 32
19	Literal
20	ExprTuple	39, 24
21	Operation	operator: 25 operands: 26
22	ExprRange	lambda_map: 27 start_index: 34 end_index: 35
23	Operation	operator: 28 operands: 29
24	Literal
25	Literal
26	ExprTuple	30
27	Lambda	parameter: 42 body: 31
28	Literal
29	ExprTuple	38, 32
30	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
31	Operation	operator: 36 operands: 37
32	Literal
33	Lambda	parameter: 42 body: 38
34	Literal
35	Variable
36	Literal
37	ExprTuple	38, 39
38	IndexedVar	variable: 40 index: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable