Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([a_1_to_m, b], 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}, a_{2}, \ldots, a_{m}, b\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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