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Expression of type Exists

from the theory of proveit.logic.sets.unification

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 Q__y_1_to_n, R__y_1_to_n, S_1_to_n, y_1_to_n
from proveit.logic import Exists, InSet
In [2]:
# build up the expression from sub-expressions
expr = Exists(instance_param_or_params = [y_1_to_n], instance_expr = InSet(x, R__y_1_to_n), domains = [S_1_to_n], condition = Q__y_1_to_n)
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())
\exists_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(x \in R\left(y_{1}, y_{2}, \ldots, y_{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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 17
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 20
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple12, 13
10Variable
11Operationoperator: 14
operands: 17
12ExprRangelambda_map: 15
start_index: 23
end_index: 24
13Operationoperator: 16
operands: 17
14Variable
15Lambdaparameter: 30
body: 18
16Variable
17ExprTuple19
18Operationoperator: 20
operands: 21
19ExprRangelambda_map: 22
start_index: 23
end_index: 24
20Literal
21ExprTuple26, 25
22Lambdaparameter: 30
body: 26
23Literal
24Variable
25IndexedVarvariable: 27
index: 30
26IndexedVarvariable: 28
index: 30
27Variable
28Variable
29ExprTuple30
30Variable