Expression of type Conditional

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, 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 = 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\{\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()

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