Expression of type Conditional

from the theory of proveit.numbers.divisibility

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, a, k, n
from proveit.logic import And, InSet
from proveit.numbers import Divides, Exp, Integer, NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Divides(k, a), And(InSet(k, Integer), InSet(a, Integer), InSet(n, NaturalPos), Divides(Exp(k, n), Exp(a, n))))

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\{k \rvert a \textrm{ if } k \in \mathbb{Z} ,  a \in \mathbb{Z} ,  n \in \mathbb{N}^+ ,  k^{n} \rvert a^{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: 14 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	23, 24
4	Literal
5	ExprTuple	6, 7, 8, 9
6	Operation	operator: 12 operands: 10
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	ExprTuple	23, 16
11	ExprTuple	24, 16
12	Literal
13	ExprTuple	25, 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	Literal
18	Operation	operator: 21 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	23, 25
21	Literal
22	ExprTuple	24, 25
23	Variable
24	Variable
25	Variable