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 And, Equals, InSet
from proveit.numbers import Complex, Mult, one, sqrt

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = ExprTuple(Lambda([a_1_to_n], Conditional(Equals(sqrt(Mult(a_1_to_n)), Mult(ExprRange(sub_expr1, sqrt(sub_expr2), one, n))), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, n)))))

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(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \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) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) \land  \left(a_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{C}\right)\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: 19 body: 2
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
9	Operation	operator: 28 operands: 12
10	Operation	operator: 18 operands: 13
11	ExprRange	lambda_map: 14 start_index: 37 end_index: 27
12	ExprTuple	15, 31
13	ExprTuple	16
14	Lambda	parameter: 36 body: 17
15	Operation	operator: 18 operands: 19
16	ExprRange	lambda_map: 20 start_index: 37 end_index: 27
17	Operation	operator: 21 operands: 22
18	Literal
19	ExprTuple	23
20	Lambda	parameter: 36 body: 24
21	Literal
22	ExprTuple	30, 25
23	ExprRange	lambda_map: 26 start_index: 37 end_index: 27
24	Operation	operator: 28 operands: 29
25	Literal
26	Lambda	parameter: 36 body: 30
27	Variable
28	Literal
29	ExprTuple	30, 31
30	IndexedVar	variable: 32 index: 36
31	Operation	operator: 34 operands: 35
32	Variable
33	ExprTuple	36
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Literal
38	Literal