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Expression of type Forall

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 theta
from proveit.logic import Forall, InSet
from proveit.numbers import IntervalCO, IntervalOO, Neg, one, pi, zero
from proveit.trigonometry import Sin
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [theta], instance_expr = InSet(Sin(theta), IntervalCO(Neg(one), zero)), domain = IntervalOO(Neg(pi), zero))
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())
\forall_{\theta \in \left(-\pi,0\right)}~\left(\sin{\theta} \in \left[-1,0\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 19
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple19, 12
10Operationoperator: 13
operand: 19
11Operationoperator: 15
operands: 16
12Operationoperator: 17
operands: 18
13Literal
14ExprTuple19
15Literal
16ExprTuple20, 22
17Literal
18ExprTuple21, 22
19Variable
20Operationoperator: 24
operand: 26
21Operationoperator: 24
operand: 27
22Literal
23ExprTuple26
24Literal
25ExprTuple27
26Literal
27Literal