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Expression of type Forall

from the theory of proveit.logic.sets.enumeration

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 n, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Boolean, Forall, InSet, Set
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = InSet(InSet(x, Set(y_1_to_n)), Boolean)), domain = Natural)
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_{n \in \mathbb{N}}~\left[\forall_{x, y_{1}, y_{2}, \ldots, y_{n}}~\left(\left(x \in \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) \in \mathbb{B}\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: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 26
body: 4
3ExprTuple26
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 17
operands: 9
7Literal
8ExprTuple10
9ExprTuple26, 11
10Lambdaparameters: 12
body: 13
11Literal
12ExprTuple19, 23
13Operationoperator: 17
operands: 14
14ExprTuple15, 16
15Operationoperator: 17
operands: 18
16Literal
17Literal
18ExprTuple19, 20
19Variable
20Operationoperator: 21
operands: 22
21Literal
22ExprTuple23
23ExprRangelambda_map: 24
start_index: 25
end_index: 26
24Lambdaparameter: 30
body: 27
25Literal
26Variable
27IndexedVarvariable: 28
index: 30
28Variable
29ExprTuple30
30Variable