Theorem ceil_of_real_above_int of type Forall

from the theory of proveit.numbers.rounding

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.rounding import ceil_of_real_above_int

# check that the built expression is the same as the stored expression
assert ceil_of_real_above_int.expr == stored_expr
assert ceil_of_real_above_int.expr._style_id == stored_expr._style_id
print("Passed sanity check: ceil_of_real_above_int matches stored_expr")

Passed sanity check: ceil_of_real_above_int matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{x \in \mathbb{Z}, y \in \mathbb{R}~|~x < y}~\left(\left(x + 1\right) \leq \left\lceil y\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	parameters: 24 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operand: 29
13	Operation	operator: 21 operands: 20
14	Operation	operator: 21 operands: 22
15	Operation	operator: 23 operands: 24
16	Literal
17	ExprTuple	28, 25
18	Literal
19	ExprTuple	29
20	ExprTuple	28, 26
21	Literal
22	ExprTuple	29, 27
23	Literal
24	ExprTuple	28, 29
25	Literal
26	Literal
27	Literal
28	Variable
29	Variable