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Expression of type Forall

from the theory of proveit.logic.sets.intersection

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 x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Forall, Intersect, NotInSet
from proveit.logic.sets import x_notin_some_A
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = NotInSet(x, Intersect(A_1_to_m)), condition = x_notin_some_A)
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, A_{1}, A_{2}, \ldots, A_{m}~|~\left(x \notin A_{1}\right) \lor  \left(x \notin A_{2}\right) \lor  \ldots \lor  \left(x \notin A_{m}\right)}~\left(x \notin \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\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
3Lambdaparameters: 4
body: 5
4ExprTuple23, 16
5Conditionalvalue: 6
condition: 7
6Operationoperator: 21
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple23, 11
9Literal
10ExprTuple12
11Operationoperator: 13
operands: 14
12ExprRangelambda_map: 15
start_index: 19
end_index: 20
13Literal
14ExprTuple16
15Lambdaparameter: 27
body: 17
16ExprRangelambda_map: 18
start_index: 19
end_index: 20
17Operationoperator: 21
operands: 22
18Lambdaparameter: 27
body: 24
19Literal
20Variable
21Literal
22ExprTuple23, 24
23Variable
24IndexedVarvariable: 25
index: 27
25Variable
26ExprTuple27
27Variable