Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\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	26, 27, 28
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	26, 27
7	Literal
8	ExprTuple	9, 10, 11, 12
9	Operation	operator: 15 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	26, 19
14	ExprTuple	27, 19
15	Literal
16	ExprTuple	28, 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	Literal
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 28
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Variable