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Expression of type Lambda

from the theory of proveit.logic.booleans.quantification.existence

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 Lambda, P, Q, alpha
from proveit.core_expr_types import P__x_1_to_n, Q__x_1_to_n, x_1_to_n
from proveit.logic import And, Forall, Implies
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy
In [2]:
# build up the expression from sub-expressions
expr = Lambda([P, Q], Implies(And(general_exists_Py_st_Qy, Forall(instance_param_or_params = [x_1_to_n], instance_expr = Implies(P__x_1_to_n, alpha), condition = Q__x_1_to_n)), alpha))
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, Q\right) \mapsto \left(\left(\left[\exists_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right] \land \left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow \alpha\right)\right]\right) \Rightarrow \alpha\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
1ExprTuple29, 24
2Operationoperator: 22
operands: 3
3ExprTuple4, 27
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8
7Operationoperator: 9
operand: 13
8Operationoperator: 11
operand: 14
9Literal
10ExprTuple13
11Literal
12ExprTuple14
13Lambdaparameters: 21
body: 15
14Lambdaparameters: 30
body: 16
15Conditionalvalue: 17
condition: 18
16Conditionalvalue: 19
condition: 20
17Operationoperator: 29
operands: 21
18Operationoperator: 24
operands: 21
19Operationoperator: 22
operands: 23
20Operationoperator: 24
operands: 30
21ExprTuple25
22Literal
23ExprTuple26, 27
24Variable
25ExprRangelambda_map: 28
start_index: 35
end_index: 36
26Operationoperator: 29
operands: 30
27Variable
28Lambdaparameter: 40
body: 31
29Variable
30ExprTuple32
31IndexedVarvariable: 33
index: 40
32ExprRangelambda_map: 34
start_index: 35
end_index: 36
33Variable
34Lambdaparameter: 40
body: 37
35Literal
36Variable
37IndexedVarvariable: 38
index: 40
38Variable
39ExprTuple40
40Variable