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Expression of type Lambda

from the theory of proveit.logic.booleans.quantification

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 B, Conditional, ExprRange, IndexedVar, Lambda, Variable, n, y
from proveit.core_expr_types import P__y_1_to_n, Q__y_1_to_n, y_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([y_1_to_n], Conditional(P__y_1_to_n, And(ExprRange(sub_expr1, InSet(IndexedVar(y, sub_expr1), B), one, n), 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())
\left(y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } \left(y_{1} \in B\right) ,  \left(y_{2} \in B\right) ,  \ldots ,  \left(y_{n} \in B\right) ,  Q\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: 11
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 11
3Operationoperator: 5
operands: 6
4Variable
5Literal
6ExprTuple7, 8
7ExprRangelambda_map: 9
start_index: 17
end_index: 18
8Operationoperator: 10
operands: 11
9Lambdaparameter: 23
body: 12
10Variable
11ExprTuple13
12Operationoperator: 14
operands: 15
13ExprRangelambda_map: 16
start_index: 17
end_index: 18
14Literal
15ExprTuple20, 19
16Lambdaparameter: 23
body: 20
17Literal
18Variable
19Variable
20IndexedVarvariable: 21
index: 23
21Variable
22ExprTuple23
23Variable