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Expression of type Lambda

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, Lambda, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import InSet, Set
from proveit.logic.sets import x_equals_any_y
In [2]:
# build up the expression from sub-expressions
expr = Lambda([x, y_1_to_n], Conditional(x_equals_any_y, InSet(x, Set(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())
\left(x, y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{\left(x = y_{1}\right) \lor  \left(x = y_{2}\right) \lor  \ldots \lor  \left(x = y_{n}\right) \textrm{ if } x \in \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple21, 15
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple21, 10
9ExprRangelambda_map: 11
start_index: 19
end_index: 20
10Operationoperator: 12
operands: 13
11Lambdaparameter: 25
body: 14
12Literal
13ExprTuple15
14Operationoperator: 16
operands: 17
15ExprRangelambda_map: 18
start_index: 19
end_index: 20
16Literal
17ExprTuple21, 22
18Lambdaparameter: 25
body: 22
19Literal
20Variable
21Variable
22IndexedVarvariable: 23
index: 25
23Variable
24ExprTuple25
25Variable