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Expression of type Lambda

from the theory of proveit.logic.equality

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, P
from proveit.core_expr_types import P__x_1_to_n, P__y_1_to_n, x_1_to_n, x_eq_y__1_to_n, y_1_to_n
from proveit.logic import And
In [2]:
# build up the expression from sub-expressions
expr = Lambda([P, x_1_to_n, y_1_to_n], Conditional(P__y_1_to_n, And(P__x_1_to_n, x_eq_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(P, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } P\left(x_{1}, x_{2}, \ldots, x_{n}\right), \left(x_{1} = y_{1}\right) ,  \left(x_{2} = y_{2}\right) ,  \ldots ,  \left(x_{n} = 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
1ExprTuple12, 15, 8
2Conditionalvalue: 3
condition: 4
3Operationoperator: 12
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8
6Literal
7ExprTuple9, 10
8ExprRangelambda_map: 11
start_index: 18
end_index: 19
9Operationoperator: 12
operands: 13
10ExprRangelambda_map: 14
start_index: 18
end_index: 19
11Lambdaparameter: 27
body: 23
12Variable
13ExprTuple15
14Lambdaparameter: 27
body: 16
15ExprRangelambda_map: 17
start_index: 18
end_index: 19
16Operationoperator: 20
operands: 21
17Lambdaparameter: 27
body: 22
18Literal
19Variable
20Literal
21ExprTuple22, 23
22IndexedVarvariable: 24
index: 27
23IndexedVarvariable: 25
index: 27
24Variable
25Variable
26ExprTuple27
27Variable