Expression of type Lambda

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, Lambda, 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 = Lambda([k, a, n], 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, a, n\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	25, 26, 27
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	25, 26
6	Literal
7	ExprTuple	8, 9, 10, 11
8	Operation	operator: 14 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	25, 18
13	ExprTuple	26, 18
14	Literal
15	ExprTuple	27, 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	Literal
20	Operation	operator: 23 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 27
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Variable
27	Variable