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 Lambda, x, y
from proveit.logic import Equals, InSet
from proveit.numbers import Divides, Integer, frac

# build up the expression from sub-expressions
expr = Lambda([x, y], Equals(Divides(x, y), InSet(frac(y, x), Integer)))

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, y\right) \mapsto \left(\left(x \rvert y\right) = \left(\frac{y}{x} \in \mathbb{Z}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 7 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	15, 14
8	Literal
9	ExprTuple	10, 11
10	Operation	operator: 12 operands: 13
11	Literal
12	Literal
13	ExprTuple	14, 15
14	Variable
15	Variable