Expression of type Conditional

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 Conditional, a, x, y
from proveit.logic import Forall, InSet
from proveit.numbers import LessEq, RealNonPos, RealPos, frac

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y], instance_expr = LessEq(frac(a, x), frac(a, y)), domain = RealPos, condition = LessEq(x, y)), InSet(a, RealNonPos))

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())

\left\{\forall_{x, y \in \mathbb{R}^+~|~x \leq y}~\left(\frac{a}{x} \leq \frac{a}{y}\right) \textrm{ if } a \in \mathbb{R}^{\le 0}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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