Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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