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 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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