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 b_1_to_m
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Exp, RealPos, one
from proveit.numbers.exponentiation import prod_a_raise_bi__1_to_m

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a, b_1_to_m], Conditional(Equals(prod_a_raise_bi__1_to_m, Exp(a, Add(b_1_to_m))), And(InSet(a, Complex), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), RealPos), one, m)))))

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, b_{1}, b_{2}, \ldots, b_{m}\right) \mapsto \left\{\left(a^{b_{1}} \cdot  a^{b_{2}} \cdot  \ldots \cdot  a^{b_{m}}\right) = a^{b_{1} +  b_{2} +  \ldots +  b_{m}} \textrm{ if } a \in \mathbb{C}, \left(b_{1} \in \mathbb{R}^+\right) ,  \left(b_{2} \in \mathbb{R}^+\right) ,  \ldots ,  \left(b_{m} \in \mathbb{R}^+\right)\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	36, 29
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: 14 operands: 15
11	Operation	operator: 31 operands: 16
12	Operation	operator: 26 operands: 17
13	ExprRange	lambda_map: 18 start_index: 34 end_index: 35
14	Literal
15	ExprTuple	19
16	ExprTuple	36, 20
17	ExprTuple	36, 21
18	Lambda	parameter: 40 body: 22
19	ExprRange	lambda_map: 23 start_index: 34 end_index: 35
20	Operation	operator: 24 operands: 25
21	Literal
22	Operation	operator: 26 operands: 27
23	Lambda	parameter: 40 body: 28
24	Literal
25	ExprTuple	29
26	Literal
27	ExprTuple	37, 30
28	Operation	operator: 31 operands: 32
29	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
30	Literal
31	Literal
32	ExprTuple	36, 37
33	Lambda	parameter: 40 body: 37
34	Literal
35	Variable
36	Variable
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable