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, x, y, z
from proveit.logic import And, Equals, InSet
from proveit.numbers import Divides, GCD, Integer, Mult, one

# build up the expression from sub-expressions
expr = Conditional(Divides(x, z), And(InSet(x, Integer), InSet(y, Integer), InSet(z, Integer), Divides(x, Mult(y, z)), Equals(GCD(x, y), one)))

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 \rvert z \textrm{ if } x \in \mathbb{Z} ,  y \in \mathbb{Z} ,  z \in \mathbb{Z} ,  x \rvert \left(y \cdot z\right) ,  gcd\left(x, y\right) = 1\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: 15 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	28, 27
4	Literal
5	ExprTuple	6, 7, 8, 9, 10
6	Operation	operator: 13 operands: 11
7	Operation	operator: 13 operands: 12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operands: 18
11	ExprTuple	28, 19
12	ExprTuple	29, 19
13	Literal
14	ExprTuple	27, 19
15	Literal
16	ExprTuple	28, 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	29, 27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Variable
29	Variable