Expression of type Forall

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 ExprRange, IndexedVar, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Mult, one, sqrt

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = 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)

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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