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, k, m
from proveit.core_expr_types import k_1_to_m
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Exp, NaturalPos, one
from proveit.numbers.exponentiation import prod_a_raise_ki__1_to_m

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(prod_a_raise_ki__1_to_m, Exp(a, Add(k_1_to_m))), And(InSet(a, Complex), ExprRange(sub_expr1, InSet(IndexedVar(k, sub_expr1), NaturalPos), 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^{k_{1}} \cdot  a^{k_{2}} \cdot  \ldots \cdot  a^{k_{m}}\right) = a^{k_{1} +  k_{2} +  \ldots +  k_{m}} \textrm{ if } a \in \mathbb{C}, \left(k_{1} \in \mathbb{N}^+\right) ,  \left(k_{2} \in \mathbb{N}^+\right) ,  \ldots ,  \left(k_{m} \in \mathbb{N}^+\right)\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: 11 operands: 12
8	Operation	operator: 28 operands: 13
9	Operation	operator: 23 operands: 14
10	ExprRange	lambda_map: 15 start_index: 31 end_index: 32
11	Literal
12	ExprTuple	16
13	ExprTuple	33, 17
14	ExprTuple	33, 18
15	Lambda	parameter: 37 body: 19
16	ExprRange	lambda_map: 20 start_index: 31 end_index: 32
17	Operation	operator: 21 operands: 22
18	Literal
19	Operation	operator: 23 operands: 24
20	Lambda	parameter: 37 body: 25
21	Literal
22	ExprTuple	26
23	Literal
24	ExprTuple	34, 27
25	Operation	operator: 28 operands: 29
26	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
27	Literal
28	Literal
29	ExprTuple	33, 34
30	Lambda	parameter: 37 body: 34
31	Literal
32	Variable
33	Variable
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable