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 LessEq, Mult, Neg, RealNonPos, frac, pi, two
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [theta], instance_expr = LessEq(Sin(theta), frac(Mult(two, theta), pi)), domain = RealNonPos, condition = LessEq(Neg(theta), 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}^{\le 0}~|~\left(-\theta\right) \leq \frac{\pi}{2}}~\left(\sin{\theta} \leq \frac{2 \cdot \theta}{\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: 30 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 18 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 14 operand: 30
11	Operation	operator: 28 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	20, 31
16	Literal
17	ExprTuple	30, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Operation	operator: 26 operand: 30
23	Operation	operator: 28 operands: 29
24	Literal
25	ExprTuple	32, 30
26	Literal
27	ExprTuple	30
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Literal
32	Literal