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Expression of type Forall

from the theory of proveit.logic.classes.membership

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 C, x
from proveit.logic import Equals, Forall, InClass, Not, NotInClass
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, C], instance_expr = Equals(NotInClass(x, C), Not(InClass(x, C))))
Out[2]:
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_{x, C}~\left(\left(x \notin_{C} C\right) = (\lnot \left(x \underset{{\scriptscriptstyle c}}{\in} C\right))\right)
In [5]:
stored_expr.style_options()
Out[5]:
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()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 14
body: 4
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8
7Operationoperator: 9
operands: 14
8Operationoperator: 10
operand: 12
9Literal
10Literal
11ExprTuple12
12Operationoperator: 13
operands: 14
13Literal
14ExprTuple15, 16
15Variable
16Variable