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 b
from proveit.core_expr_types import a_1_to_m
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Exp, Mult, RealPos
from proveit.numbers.exponentiation import prod_ai_raise_b__1_to_m

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_m, b], instance_expr = Equals(Exp(Mult(a_1_to_m), b), prod_ai_raise_b__1_to_m), domains = [RealPos, 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_{\left(a_{1} \in \mathbb{R}^+\right), \left(a_{2} \in \mathbb{R}^+\right), \ldots, \left(a_{m} \in \mathbb{R}^+\right), b \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{m}\right)^{b} = \left(\left(a_{1}\right)^{b} \cdot  \left(a_{2}\right)^{b} \cdot  \ldots \cdot  \left(a_{m}\right)^{b}\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: 4 body: 5
4	ExprTuple	29, 38
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 35 operands: 16
13	Operation	operator: 24 operands: 17
14	ExprRange	lambda_map: 18 start_index: 33 end_index: 34
15	Operation	operator: 27 operands: 19
16	ExprTuple	20, 38
17	ExprTuple	21
18	Lambda	parameter: 41 body: 22
19	ExprTuple	38, 23
20	Operation	operator: 24 operands: 25
21	ExprRange	lambda_map: 26 start_index: 33 end_index: 34
22	Operation	operator: 27 operands: 28
23	Literal
24	Literal
25	ExprTuple	29
26	Lambda	parameter: 41 body: 30
27	Literal
28	ExprTuple	37, 31
29	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
30	Operation	operator: 35 operands: 36
31	Literal
32	Lambda	parameter: 41 body: 37
33	Literal
34	Variable
35	Literal
36	ExprTuple	37, 38
37	IndexedVar	variable: 39 index: 41
38	Variable
39	Variable
40	ExprTuple	41
41	Variable