Expression of type Forall

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

# build up the expression from sub-expressions
sub_expr1 = Ceil(x)
expr = Forall(instance_param_or_params = [x], instance_expr = Equals(Round(x), sub_expr1), domain = Real, condition = 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())

\forall_{x \in \mathbb{R}~|~\left(x - \left\lfloor x\right\rfloor\right) = \left(\left\lceil x\right\rceil - x\right)}~\left(round\left(x\right) = \left\lceil x\right\rceil\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 33 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 16 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 25
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 13 operand: 33
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Literal
14	Literal
15	ExprTuple	33, 18
16	Literal
17	ExprTuple	19, 20
18	Literal
19	Operation	operator: 22 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	33, 24
22	Literal
23	ExprTuple	25, 26
24	Operation	operator: 29 operand: 30
25	Operation	operator: 28 operand: 33
26	Operation	operator: 29 operand: 33
27	ExprTuple	30
28	Literal
29	Literal
30	Operation	operator: 31 operand: 33
31	Literal
32	ExprTuple	33
33	Variable