Expression of type Conditional

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, x, y
from proveit.logic import And, InSet
from proveit.numbers import Floor, Integer, LessEq, Real, greater_eq

# build up the expression from sub-expressions
expr = Conditional(greater_eq(Floor(x), y), And(InSet(x, Real), InSet(y, Integer), LessEq(y, 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())

\left\{\left\lfloor x\right\rfloor \geq y \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{Z} ,  y \leq x\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 15 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	19, 6
4	Literal
5	ExprTuple	7, 8, 9
6	Operation	operator: 10 operand: 20
7	Operation	operator: 13 operands: 12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 15 operands: 16
10	Literal
11	ExprTuple	20
12	ExprTuple	20, 17
13	Literal
14	ExprTuple	19, 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	Literal
19	Variable
20	Variable