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, Variable, n, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, Natural, one

# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(x, n), Mult(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), x, one, n))), And(InSet(x, Complex), InSet(n, Natural)))

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\{x^{n} = \left(x \cdot  x \cdot  ..\left(n - 3\right) \times.. \cdot  x\right) \textrm{ if } x \in \mathbb{C} ,  n \in \mathbb{N}\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: 13 operands: 14
9	Operation	operator: 16 operands: 15
10	Operation	operator: 16 operands: 17
11	Literal
12	ExprTuple	25, 23
13	Literal
14	ExprTuple	18
15	ExprTuple	25, 19
16	Literal
17	ExprTuple	23, 20
18	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
19	Literal
20	Literal
21	Lambda	parameter: 26 body: 25
22	Literal
23	Variable
24	ExprTuple	26
25	Variable
26	Variable