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, y
from proveit.logic import Forall
from proveit.numbers import Add, Floor, Real, greater_eq

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, y], instance_expr = greater_eq(Floor(Add(x, y)), Add(Floor(x), Floor(y))), domain = Real)

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, y \in \mathbb{R}}~\left(\left\lfloor x + y\right\rfloor \geq \left(\left\lfloor x\right\rfloor + \left\lfloor y\right\rfloor\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: 28 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
11	Operation	operator: 27 operands: 15
12	Operation	operator: 25 operand: 22
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	20, 21
16	ExprTuple	22
17	ExprTuple	29, 23
18	Literal
19	ExprTuple	30, 23
20	Operation	operator: 25 operand: 29
21	Operation	operator: 25 operand: 30
22	Operation	operator: 27 operands: 28
23	Literal
24	ExprTuple	29
25	Literal
26	ExprTuple	30
27	Literal
28	ExprTuple	29, 30
29	Variable
30	Variable