Theorem floor_of_real_below_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 floor_of_real_below_int

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

Passed sanity check: floor_of_real_below_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{R}, y \in \mathbb{Z}~|~x < y}~\left(\left\lfloor x\right\rfloor \leq \left(y - 1\right)\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 operand: 28
12	Operation	operator: 18 operands: 19
13	Operation	operator: 21 operands: 20
14	Operation	operator: 21 operands: 22
15	Operation	operator: 23 operands: 24
16	Literal
17	ExprTuple	28
18	Literal
19	ExprTuple	29, 25
20	ExprTuple	28, 26
21	Literal
22	ExprTuple	29, 27
23	Literal
24	ExprTuple	28, 29
25	Operation	operator: 30 operand: 32
26	Literal
27	Literal
28	Variable
29	Variable
30	Literal
31	ExprTuple	32
32	Literal