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Expression of type ExprTuple

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 ExprTuple, Lambda, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Equals, NotInSet, Set
from proveit.logic.sets import x_notequals_all_y
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y_1_to_n], Equals(NotInSet(x, Set(y_1_to_n)), x_notequals_all_y)))
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(\left(x, y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left(\left(x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) = \left(\left(x \neq y_{1}\right) \land  \left(x \neq y_{2}\right) \land  \ldots \land  \left(x \neq y_{n}\right)\right)\right)\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple24, 17
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple24, 12
10Literal
11ExprTuple13
12Operationoperator: 14
operands: 15
13ExprRangelambda_map: 16
start_index: 20
end_index: 21
14Literal
15ExprTuple17
16Lambdaparameter: 28
body: 18
17ExprRangelambda_map: 19
start_index: 20
end_index: 21
18Operationoperator: 22
operands: 23
19Lambdaparameter: 28
body: 25
20Literal
21Variable
22Literal
23ExprTuple24, 25
24Variable
25IndexedVarvariable: 26
index: 28
26Variable
27ExprTuple28
28Variable