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Expression of type Forall

from the theory of proveit.logic.booleans.quantification.existence

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 P, Q
from proveit.logic import Forall, Not
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx, general_forall__Py_not_T__st_Qy
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [P, Q], instance_expr = general_exists_Px_st_Qx, condition = Not(general_forall__Py_not_T__st_Qy))
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, Q~|~\lnot \left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \neq \top\right)\right]}~\left[\exists_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\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: 14
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple32, 27
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operand: 12
7Literal
8ExprTuple11
9Literal
10ExprTuple12
11Lambdaparameters: 19
body: 13
12Operationoperator: 14
operand: 18
13Conditionalvalue: 16
condition: 17
14Literal
15ExprTuple18
16Operationoperator: 32
operands: 19
17Operationoperator: 27
operands: 19
18Lambdaparameters: 33
body: 20
19ExprTuple21
20Conditionalvalue: 22
condition: 23
21ExprRangelambda_map: 24
start_index: 36
end_index: 37
22Operationoperator: 25
operands: 26
23Operationoperator: 27
operands: 33
24Lambdaparameter: 41
body: 28
25Literal
26ExprTuple29, 30
27Variable
28IndexedVarvariable: 31
index: 41
29Operationoperator: 32
operands: 33
30Literal
31Variable
32Variable
33ExprTuple34
34ExprRangelambda_map: 35
start_index: 36
end_index: 37
35Lambdaparameter: 41
body: 38
36Literal
37Variable
38IndexedVarvariable: 39
index: 41
39Variable
40ExprTuple41
41Variable