Expression of type ExprTuple

from the theory of proveit.numbers.rounding

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
from proveit.logic import And, InSet
from proveit.numbers import Abs, Integer, LessEq, Real, Round, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y], Conditional(LessEq(Abs(subtract(Round(x), x)), Abs(subtract(y, x))), And(InSet(x, Real), InSet(y, 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(\left(x, y\right) \mapsto \left\{\left|round\left(x\right) - x\right| \leq \left|y - x\right| \textrm{ if } x \in \mathbb{R} ,  y \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	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	33, 28
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 15 operand: 20
11	Operation	operator: 15 operand: 21
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	20
15	Literal
16	ExprTuple	21
17	ExprTuple	33, 22
18	Literal
19	ExprTuple	28, 23
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	27, 29
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 30 operand: 33
28	Variable
29	Operation	operator: 31 operand: 33
30	Literal
31	Literal
32	ExprTuple	33
33	Variable