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 Add, Ceil, Real, greater_eq, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y], Conditional(greater_eq(Ceil(Add(x, y)), subtract(Add(Ceil(x), Ceil(y)), one)), And(InSet(x, Real), InSet(y, Real)))))

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\lceil x + y\right\rceil \geq \left(\left(\left\lceil x\right\rceil + \left\lceil y\right\rceil\right) - 1\right) \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R}\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: 26 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 25 operands: 13
10	Operation	operator: 31 operand: 20
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 19
14	ExprTuple	20
15	ExprTuple	33, 21
16	Literal
17	ExprTuple	34, 21
18	Operation	operator: 25 operands: 22
19	Operation	operator: 23 operand: 29
20	Operation	operator: 25 operands: 26
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29
25	Literal
26	ExprTuple	33, 34
27	Operation	operator: 31 operand: 33
28	Operation	operator: 31 operand: 34
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	Variable
34	Variable