Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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