Expression of type Conditional

from the theory of proveit.numbers.exponentiation

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 And, InSet
from proveit.numbers import Exp, Less, LessEq, Real, zero

# build up the expression from sub-expressions
expr = Conditional(LessEq(Exp(y, a), Exp(x, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), And(Less(zero, x), LessEq(x, y)).with_total_ordering_style(), Less(a, zero)))

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^{a} \leq x^{a} \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  0 < x \leq y ,  a < 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: 28 operands: 3
2	Operation	operator: 19 operands: 4
3	ExprTuple	5, 6
4	ExprTuple	7, 8, 9, 10, 11
5	Operation	operator: 13 operands: 12
6	Operation	operator: 13 operands: 14
7	Operation	operator: 17 operands: 15
8	Operation	operator: 17 operands: 16
9	Operation	operator: 17 operands: 18
10	Operation	operator: 19 operands: 20
11	Operation	operator: 26 operands: 21
12	ExprTuple	32, 25
13	Literal
14	ExprTuple	31, 25
15	ExprTuple	25, 22
16	ExprTuple	31, 22
17	Literal
18	ExprTuple	32, 22
19	Literal
20	ExprTuple	23, 24
21	ExprTuple	25, 30
22	Literal
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	Variable
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	31, 32
30	Literal
31	Variable
32	Variable