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
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Floor, Real, Round, frac, one, two

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(Round(x), Floor(Add(x, frac(one, two)))), InSet(x, 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())

x \mapsto \left\{round\left(x\right) = \left\lfloor x + \frac{1}{2}\right\rfloor \textrm{ if } x \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	parameter: 18 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	18, 10
8	Operation	operator: 11 operand: 18
9	Operation	operator: 13 operand: 15
10	Literal
11	Literal
12	ExprTuple	18
13	Literal
14	ExprTuple	15
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	18, 19
18	Variable
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Literal
23	Literal