Expression of type Conditional

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

# build up the expression from sub-expressions
expr = Conditional(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]), InSet(m, 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())

\left\{\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) \textrm{ if } m \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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