Theorem exp_nonpos_less of type Forall

from the theory of proveit.numbers.exponentiation

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.exponentiation import exp_nonpos_less

# check that the built expression is the same as the stored expression
assert exp_nonpos_less.expr == stored_expr
assert exp_nonpos_less.expr._style_id == stored_expr._style_id
print("Passed sanity check: exp_nonpos_less matches stored_expr")

Passed sanity check: exp_nonpos_less matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{a, x, y \in \mathbb{R}~|~0 < x < y, a \leq 0}~\left(y^{a} \leq x^{a}\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: 4 body: 5
4	ExprTuple	31, 36, 37
5	Conditional	value: 6 condition: 7
6	Operation	operator: 26 operands: 8
7	Operation	operator: 24 operands: 9
8	ExprTuple	10, 11
9	ExprTuple	12, 13, 14, 15, 16
10	Operation	operator: 18 operands: 17
11	Operation	operator: 18 operands: 19
12	Operation	operator: 22 operands: 20
13	Operation	operator: 22 operands: 21
14	Operation	operator: 22 operands: 23
15	Operation	operator: 24 operands: 25
16	Operation	operator: 26 operands: 27
17	ExprTuple	37, 31
18	Literal
19	ExprTuple	36, 31
20	ExprTuple	31, 28
21	ExprTuple	36, 28
22	Literal
23	ExprTuple	37, 28
24	Literal
25	ExprTuple	29, 30
26	Literal
27	ExprTuple	31, 35
28	Literal
29	Operation	operator: 33 operands: 32
30	Operation	operator: 33 operands: 34
31	Variable
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	36, 37
35	Literal
36	Variable
37	Variable