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, RealNonNeg, frac, greater_eq, pi, two
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = Lambda(theta, Conditional(greater_eq(Sin(theta), frac(Mult(two, theta), pi)), And(InSet(theta, RealNonNeg), LessEq(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} \geq \frac{2 \cdot \theta}{\pi} \textrm{ if } \theta \in \mathbb{R}^{\ge 0} ,  \theta \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: 25 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 16 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 23 operands: 11
8	Operation	operator: 12 operand: 25
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprTuple	18, 26
12	Literal
13	ExprTuple	25
14	Literal
15	ExprTuple	25, 19
16	Literal
17	ExprTuple	25, 20
18	Operation	operator: 21 operands: 22
19	Literal
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	27, 25
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Literal
27	Literal