Expression of type Forall

from the theory of proveit.numbers.division

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 a, x, y
from proveit.logic import Forall
from proveit.numbers import LessEq, RealNeg, RealNonNeg, frac, greater_eq

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a], instance_expr = Forall(instance_param_or_params = [x, y], instance_expr = greater_eq(frac(a, x), frac(a, y)), domain = RealNeg, condition = LessEq(x, y)), domain = RealNonNeg)

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_{a \in \mathbb{R}^{\ge 0}}~\left[\forall_{x, y \in \mathbb{R}^-~|~x \leq y}~\left(\frac{a}{x} \geq \frac{a}{y}\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 31 body: 4
3	ExprTuple	31
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 27 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	31, 11
10	Lambda	parameters: 30 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 29 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 24 operands: 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 27 operands: 26
21	Operation	operator: 27 operands: 28
22	Operation	operator: 29 operands: 30
23	ExprTuple	31, 34
24	Literal
25	ExprTuple	31, 33
26	ExprTuple	33, 32
27	Literal
28	ExprTuple	34, 32
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Literal
33	Variable
34	Variable