logo

Expression of type Forall

from the theory of proveit.logic.booleans

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 A, P, PofA
from proveit.logic import Boolean, Equals, Forall, PofFalse, PofTrue, TRUE
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [P], instance_expr = Equals(Forall(instance_param_or_params = [A], instance_expr = PofA, domain = Boolean), TRUE), conditions = [Equals(PofTrue, TRUE), Equals(PofFalse, TRUE)])
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_{P~|~P\left(\top\right) = \top, P\left(\bot\right) = \top}~\left(\left[\forall_{A \in \mathbb{B}}~P\left(A\right)\right] = \top\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: 13
operand: 2
1ExprTuple2
2Lambdaparameter: 28
body: 4
3ExprTuple28
4Conditionalvalue: 5
condition: 6
5Operationoperator: 16
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 26
8Literal
9ExprTuple11, 12
10Operationoperator: 13
operand: 18
11Operationoperator: 16
operands: 15
12Operationoperator: 16
operands: 17
13Literal
14ExprTuple18
15ExprTuple19, 26
16Literal
17ExprTuple20, 26
18Lambdaparameter: 32
body: 21
19Operationoperator: 28
operand: 26
20Operationoperator: 28
operand: 27
21Conditionalvalue: 24
condition: 25
22ExprTuple26
23ExprTuple27
24Operationoperator: 28
operand: 32
25Operationoperator: 30
operands: 31
26Literal
27Literal
28Variable
29ExprTuple32
30Literal
31ExprTuple32, 33
32Variable
33Literal