Expression of type And

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 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 = 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 \in \mathbb{Z}\right) \land \left(y \in \mathbb{Z}\right) \land \left(z \in \mathbb{Z}\right) \land \left(x \rvert \left(y \cdot z\right)\right) \land \left(gcd\left(x, y\right) = 1\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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