Expression of type Lambda

from the theory of proveit.numbers.integration

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, b, l
from proveit.logic import And, InSet
from proveit.numbers import Exp, Integrate, IntervalCC, LessEq, RealPos, frac, one, two

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(LessEq(Integrate(index_or_indices = [l], integrand = frac(one, Exp(l, two)), domain = IntervalCC(a, b)), frac(one, a)), And(InSet(a, RealPos), InSet(b, RealPos), LessEq(a, b))))

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, b\right) \mapsto \left\{\left(\int_{a}^{b} \frac{1}{l^{2}}\,dl\right) \leq \frac{1}{a} \textrm{ if } a \in \mathbb{R}^+ ,  b \in \mathbb{R}^+ ,  a \leq b\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 34 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 17 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 12 operand: 18
8	Operation	operator: 24 operands: 14
9	Operation	operator: 26 operands: 15
10	Operation	operator: 26 operands: 16
11	Operation	operator: 17 operands: 34
12	Literal
13	ExprTuple	18
14	ExprTuple	28, 37
15	ExprTuple	37, 19
16	ExprTuple	38, 19
17	Literal
18	Lambda	parameter: 35 body: 21
19	Literal
20	ExprTuple	35
21	Conditional	value: 22 condition: 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	35, 30
28	Literal
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operands: 34
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37, 38
35	Variable
36	Literal
37	Variable
38	Variable