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 And, Equals, InSet
from proveit.numbers import Ceil, Floor, Real, Round, subtract

# build up the expression from sub-expressions
sub_expr1 = Ceil(x)
expr = Lambda(x, Conditional(Equals(Round(x), sub_expr1), And(InSet(x, Real), Equals(subtract(x, Floor(x)), subtract(sub_expr1, x)))))

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\lceil x\right\rceil \textrm{ if } x \in \mathbb{R} ,  \left(x - \left\lfloor x\right\rfloor\right) = \left(\left\lceil x\right\rceil - x\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 30 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 13 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 22
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operand: 30
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	Literal
11	Literal
12	ExprTuple	30, 15
13	Literal
14	ExprTuple	16, 17
15	Literal
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	30, 21
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 26 operand: 27
22	Operation	operator: 25 operand: 30
23	Operation	operator: 26 operand: 30
24	ExprTuple	27
25	Literal
26	Literal
27	Operation	operator: 28 operand: 30
28	Literal
29	ExprTuple	30
30	Variable