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Expression of type ExprTuple

from the theory of proveit.trigonometry

In [1]:
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, ExprTuple, 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
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(theta, Conditional(greater_eq(Sin(theta), frac(Mult(two, theta), pi)), And(InSet(theta, RealNonNeg), LessEq(theta, frac(pi, two))))))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\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..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 26
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 17
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11
8Operationoperator: 24
operands: 12
9Operationoperator: 13
operand: 26
10Operationoperator: 15
operands: 16
11Operationoperator: 17
operands: 18
12ExprTuple19, 27
13Literal
14ExprTuple26
15Literal
16ExprTuple26, 20
17Literal
18ExprTuple26, 21
19Operationoperator: 22
operands: 23
20Literal
21Operationoperator: 24
operands: 25
22Literal
23ExprTuple28, 26
24Literal
25ExprTuple27, 28
26Variable
27Literal
28Literal