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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 Conditional, Lambda
from proveit.core_expr_types import P__x_1_to_m_y_1_to_n, Q__x_1_to_m, R__x_1_to_m_y_1_to_n, x_1_to_m, y_1_to_n
from proveit.logic import And
In [2]:
# build up the expression from sub-expressions
expr = Lambda([x_1_to_m, y_1_to_n], Conditional(P__x_1_to_m_y_1_to_n, And(Q__x_1_to_m, R__x_1_to_m_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_{1}, x_{2}, \ldots, x_{m}, y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } Q\left(x_{1}, x_{2}, \ldots, x_{m}\right) ,  R\left(x_{1}, x_{2}, \ldots, x_{m},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: 12
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 12
3Operationoperator: 5
operands: 6
4Variable
5Literal
6ExprTuple7, 8
7Operationoperator: 9
operands: 10
8Operationoperator: 11
operands: 12
9Variable
10ExprTuple13
11Variable
12ExprTuple13, 14
13ExprRangelambda_map: 15
start_index: 18
end_index: 16
14ExprRangelambda_map: 17
start_index: 18
end_index: 19
15Lambdaparameter: 25
body: 20
16Variable
17Lambdaparameter: 25
body: 21
18Literal
19Variable
20IndexedVarvariable: 22
index: 25
21IndexedVarvariable: 23
index: 25
22Variable
23Variable
24ExprTuple25
25Variable