Expression of type ExprTuple

from the theory of proveit.numbers.exponentiation

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, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Mult, NaturalPos, one, sqrt

# 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 = [a_1_to_n], instance_expr = Equals(sqrt(Mult(a_1_to_n)), Mult(ExprRange(sub_expr1, sqrt(IndexedVar(a, sub_expr1)), one, n))), domain = Complex), 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_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{C}}~\left(\sqrt{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right)} = \left(\sqrt{\left(a_{1}\right)} \cdot  \sqrt{\left(a_{2}\right)} \cdot  \ldots \cdot  \sqrt{\left(a_{n}\right)}\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: 36 body: 3
2	ExprTuple	36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 30 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	36, 10
9	Lambda	parameters: 28 body: 11
10	Literal
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
18	Operation	operator: 37 operands: 21
19	Operation	operator: 27 operands: 22
20	ExprRange	lambda_map: 23 start_index: 46 end_index: 36
21	ExprTuple	24, 40
22	ExprTuple	25
23	Lambda	parameter: 45 body: 26
24	Operation	operator: 27 operands: 28
25	ExprRange	lambda_map: 29 start_index: 46 end_index: 36
26	Operation	operator: 30 operands: 31
27	Literal
28	ExprTuple	32
29	Lambda	parameter: 45 body: 33
30	Literal
31	ExprTuple	39, 34
32	ExprRange	lambda_map: 35 start_index: 46 end_index: 36
33	Operation	operator: 37 operands: 38
34	Literal
35	Lambda	parameter: 45 body: 39
36	Variable
37	Literal
38	ExprTuple	39, 40
39	IndexedVar	variable: 41 index: 45
40	Operation	operator: 43 operands: 44
41	Variable
42	ExprTuple	45
43	Literal
44	ExprTuple	46, 47
45	Variable
46	Literal
47	Literal