Expression of type And

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

# build up the expression from sub-expressions
expr = And(InSet(x, Real), Equals(subtract(x, Floor(x)), subtract(Ceil(x), 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(x \in \mathbb{R}\right) \land \left(\left(x - \left\lfloor x\right\rfloor\right) = \left(\left\lceil x\right\rceil - x\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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