Expression of type Lambda

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 Conditional, Lambda, theta
from proveit.logic import And, InSet
from proveit.numbers import LessEq, Mult, Neg, RealNonPos, frac, pi, two
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = Lambda(theta, Conditional(LessEq(Sin(theta), frac(Mult(two, theta), pi)), And(InSet(theta, RealNonPos), 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())

\theta \mapsto \left\{\sin{\theta} \leq \frac{2 \cdot \theta}{\pi} \textrm{ if } \theta \in \mathbb{R}^{\le 0} ,  \left(-\theta\right) \leq \frac{\pi}{2}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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