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Expression of type Conditional

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 Conditional, n, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Boolean, Forall, InSet, NotInSet, Set
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = InSet(NotInSet(x, Set(y_1_to_n)), Boolean)), InSet(n, 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())
\left\{\forall_{x, y_{1}, y_{2}, \ldots, y_{n}}~\left(\left(x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) \in \mathbb{B}\right) \textrm{ if } n \in \mathbb{N}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 10
operands: 5
3Literal
4ExprTuple6
5ExprTuple23, 7
6Lambdaparameters: 8
body: 9
7Literal
8ExprTuple16, 20
9Operationoperator: 10
operands: 11
10Literal
11ExprTuple12, 13
12Operationoperator: 14
operands: 15
13Literal
14Literal
15ExprTuple16, 17
16Variable
17Operationoperator: 18
operands: 19
18Literal
19ExprTuple20
20ExprRangelambda_map: 21
start_index: 22
end_index: 23
21Lambdaparameter: 27
body: 24
22Literal
23Variable
24IndexedVarvariable: 25
index: 27
25Variable
26ExprTuple27
27Variable