Expression of type Lambda

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, Lambda, x, y
from proveit.logic import And, InSet
from proveit.numbers import Add, Ceil, LessEq, Real

# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(LessEq(Ceil(Add(x, y)), Add(Ceil(x), Ceil(y))), 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(x, y\right) \mapsto \left\{\left\lceil x + y\right\rceil \leq \left(\left\lceil x\right\rceil + \left\lceil y\right\rceil\right) \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 22 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 24 operand: 17
9	Operation	operator: 21 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17
13	ExprTuple	18, 19
14	ExprTuple	26, 20
15	Literal
16	ExprTuple	27, 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 24 operand: 26
19	Operation	operator: 24 operand: 27
20	Literal
21	Literal
22	ExprTuple	26, 27
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Variable
27	Variable