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, NotEquals
from proveit.numbers import Add, Complex, Exp, Real, one, zero
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), Real), one, m), NotEquals(a, zero)))))

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) ,  a \neq 0\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	40, 33
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, 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 35 operands: 17
12	Operation	operator: 30 operands: 18
13	ExprRange	lambda_map: 19 start_index: 38 end_index: 39
14	Operation	operator: 20 operands: 21
15	Literal
16	ExprTuple	22
17	ExprTuple	40, 23
18	ExprTuple	40, 24
19	Lambda	parameter: 44 body: 25
20	Literal
21	ExprTuple	40, 26
22	ExprRange	lambda_map: 27 start_index: 38 end_index: 39
23	Operation	operator: 28 operands: 29
24	Literal
25	Operation	operator: 30 operands: 31
26	Literal
27	Lambda	parameter: 44 body: 32
28	Literal
29	ExprTuple	33
30	Literal
31	ExprTuple	41, 34
32	Operation	operator: 35 operands: 36
33	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
34	Literal
35	Literal
36	ExprTuple	40, 41
37	Lambda	parameter: 44 body: 41
38	Literal
39	Variable
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable