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, 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 = ExprTuple(Lambda([x, y, z], 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(\left(x, y, z\right) \mapsto \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..\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	31, 32, 30
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	31, 30
7	Literal
8	ExprTuple	9, 10, 11, 12, 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	Operation	operator: 20 operands: 21
14	ExprTuple	31, 22
15	ExprTuple	32, 22
16	Literal
17	ExprTuple	30, 22
18	Literal
19	ExprTuple	31, 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	Literal
26	Literal
27	ExprTuple	32, 30
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Variable
32	Variable