Expression of type Lambda

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, Lambda, a, x, y
from proveit.logic import And, InSet
from proveit.numbers import Exp, Less, LessEq, Real, greater, zero

# build up the expression from sub-expressions
expr = Lambda([a, x, y], Conditional(Less(Exp(x, a), Exp(y, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), And(LessEq(zero, x), Less(x, y)).with_total_ordering_style(), greater(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(a, x, y\right) \mapsto \left\{x^{a} < y^{a} \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  0 \leq x < y ,  a > 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	27, 33, 34
2	Conditional	value: 3 condition: 4
3	Operation	operator: 30 operands: 5
4	Operation	operator: 21 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10, 11, 12, 13
7	Operation	operator: 15 operands: 14
8	Operation	operator: 15 operands: 16
9	Operation	operator: 19 operands: 17
10	Operation	operator: 19 operands: 18
11	Operation	operator: 19 operands: 20
12	Operation	operator: 21 operands: 22
13	Operation	operator: 30 operands: 23
14	ExprTuple	33, 27
15	Literal
16	ExprTuple	34, 27
17	ExprTuple	27, 24
18	ExprTuple	33, 24
19	Literal
20	ExprTuple	34, 24
21	Literal
22	ExprTuple	25, 26
23	ExprTuple	32, 27
24	Literal
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Variable
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	33, 34
32	Literal
33	Variable
34	Variable