Expression of type Conditional

from the theory of proveit.numbers.ordering

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, x, y
from proveit.logic import And, InSet, Not
from proveit.numbers import Less, LessEq, Real

# build up the expression from sub-expressions
expr = Conditional(Less(y, x), And(InSet(x, Real), InSet(y, Real), Not(LessEq(x, y))))

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\{y < x \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R} ,  \lnot \left(x \leq y\right)\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	20, 19
5	Literal
6	ExprTuple	7, 8, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operand: 16
10	ExprTuple	19, 15
11	Literal
12	ExprTuple	20, 15
13	Literal
14	ExprTuple	16
15	Literal
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Variable