Expression of type Forall

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

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = LessEq(Integrate(index_or_indices = [l], integrand = frac(one, Exp(l, two)), domain = IntervalCC(a, b)), frac(one, a)), domain = RealPos, condition = 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())

\forall_{a, b \in \mathbb{R}^+~|~a \leq b}~\left(\left(\int_{a}^{b} \frac{1}{l^{2}}\,dl\right) \leq \frac{1}{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: 37 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 20 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 15 operand: 21
11	Operation	operator: 27 operands: 17
12	Operation	operator: 29 operands: 18
13	Operation	operator: 29 operands: 19
14	Operation	operator: 20 operands: 37
15	Literal
16	ExprTuple	21
17	ExprTuple	31, 40
18	ExprTuple	40, 22
19	ExprTuple	41, 22
20	Literal
21	Lambda	parameter: 38 body: 24
22	Literal
23	ExprTuple	38
24	Conditional	value: 25 condition: 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	38, 33
31	Literal
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operands: 37
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40, 41
38	Variable
39	Literal
40	Variable
41	Variable