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Expression of type Lambda

from the theory of proveit.logic.sets.unification

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, Q, R, x
from proveit.core_expr_types import Q__y_1_to_n, R__y_1_to_n, S_1_to_n, y_1_to_n
from proveit.logic import Equals, Exists, InSet
from proveit.logic.sets import general_unionall_Ryn
In [2]:
# build up the expression from sub-expressions
expr = Lambda([S_1_to_n, Q, R, x], Equals(InSet(x, general_unionall_Ryn), Exists(instance_param_or_params = [y_1_to_n], instance_expr = InSet(x, R__y_1_to_n), domains = [S_1_to_n], condition = Q__y_1_to_n)).with_wrapping_at(1))
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(S_{1}, S_{2}, \ldots, S_{n}, Q, R, x\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left(x \in \left[\bigcup_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~R\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right]\right) \\  = \left[\exists_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(x \in R\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right)\right] \end{array} \end{array}\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
1ExprTuple3, 30, 26, 22
2Operationoperator: 4
operands: 5
3ExprRangelambda_map: 6
start_index: 37
end_index: 38
4Literal
5ExprTuple7, 8
6Lambdaparameter: 44
body: 39
7Operationoperator: 34
operands: 9
8Operationoperator: 10
operand: 13
9ExprTuple22, 12
10Literal
11ExprTuple13
12Operationoperator: 14
operand: 17
13Lambdaparameters: 31
body: 16
14Literal
15ExprTuple17
16Conditionalvalue: 18
condition: 21
17Lambdaparameters: 31
body: 19
18Operationoperator: 34
operands: 20
19Conditionalvalue: 23
condition: 21
20ExprTuple22, 23
21Operationoperator: 24
operands: 25
22Variable
23Operationoperator: 26
operands: 31
24Literal
25ExprTuple27, 28
26Variable
27ExprRangelambda_map: 29
start_index: 37
end_index: 38
28Operationoperator: 30
operands: 31
29Lambdaparameter: 44
body: 32
30Variable
31ExprTuple33
32Operationoperator: 34
operands: 35
33ExprRangelambda_map: 36
start_index: 37
end_index: 38
34Literal
35ExprTuple40, 39
36Lambdaparameter: 44
body: 40
37Literal
38Variable
39IndexedVarvariable: 41
index: 44
40IndexedVarvariable: 42
index: 44
41Variable
42Variable
43ExprTuple44
44Variable