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 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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