Expression of type Forall

from the theory of proveit.trigonometry

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 theta
from proveit.logic import Forall
from proveit.numbers import Abs, LessEq, Mult, Real, frac, greater_eq, pi, two
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
sub_expr1 = Abs(theta)
expr = Forall(instance_param_or_params = [theta], instance_expr = greater_eq(Sin(sub_expr1), frac(Mult(two, sub_expr1), pi)), domain = Real, condition = LessEq(sub_expr1, frac(pi, two)))

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_{\theta \in \mathbb{R}~|~\left|\theta\right| \leq \frac{\pi}{2}}~\left(\sin{\left|\theta\right|} \geq \frac{2 \cdot \left|\theta\right|}{\pi}\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	parameter: 33 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 19 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 26 operands: 14
11	Operation	operator: 15 operand: 28
12	Operation	operator: 17 operands: 18
13	Operation	operator: 19 operands: 20
14	ExprTuple	21, 29
15	Literal
16	ExprTuple	28
17	Literal
18	ExprTuple	33, 22
19	Literal
20	ExprTuple	28, 23
21	Operation	operator: 24 operands: 25
22	Literal
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	30, 28
26	Literal
27	ExprTuple	29, 30
28	Operation	operator: 31 operand: 33
29	Literal
30	Literal
31	Literal
32	ExprTuple	33
33	Variable