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, ExprRange, IndexedVar, Variable, a, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, RealPos, one
from proveit.numbers.exponentiation import prod_ai_raise_b__1_to_m

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Exp(Mult(a_1_to_m), b), prod_ai_raise_b__1_to_m), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RealPos), one, m), InSet(b, 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())

\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) \textrm{ if } \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}\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 30 operands: 11
8	Operation	operator: 19 operands: 12
9	ExprRange	lambda_map: 13 start_index: 28 end_index: 29
10	Operation	operator: 22 operands: 14
11	ExprTuple	15, 33
12	ExprTuple	16
13	Lambda	parameter: 36 body: 17
14	ExprTuple	33, 18
15	Operation	operator: 19 operands: 20
16	ExprRange	lambda_map: 21 start_index: 28 end_index: 29
17	Operation	operator: 22 operands: 23
18	Literal
19	Literal
20	ExprTuple	24
21	Lambda	parameter: 36 body: 25
22	Literal
23	ExprTuple	32, 26
24	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	Lambda	parameter: 36 body: 32
28	Literal
29	Variable
30	Literal
31	ExprTuple	32, 33
32	IndexedVar	variable: 34 index: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable