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Expression of type ExprTuple

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 Conditional, ExprTuple, Lambda, Q, R, n, 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, Forall, InSet
from proveit.logic.sets import general_unionall_Ryn
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [S_1_to_n, Q, R, x], instance_expr = 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)), InSet(n, NaturalPos))))
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(n \mapsto \left\{\forall_{S_{1}, S_{2}, \ldots, S_{n}, Q, R, x}~\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) \textrm{ if } n \in \mathbb{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
0ExprTuple1
1Lambdaparameter: 48
body: 3
2ExprTuple48
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 44
operands: 8
6Literal
7ExprTuple9
8ExprTuple48, 10
9Lambdaparameters: 11
body: 12
10Literal
11ExprTuple13, 40, 36, 32
12Operationoperator: 14
operands: 15
13ExprRangelambda_map: 16
start_index: 47
end_index: 48
14Literal
15ExprTuple17, 18
16Lambdaparameter: 54
body: 49
17Operationoperator: 44
operands: 19
18Operationoperator: 20
operand: 23
19ExprTuple32, 22
20Literal
21ExprTuple23
22Operationoperator: 24
operand: 27
23Lambdaparameters: 41
body: 26
24Literal
25ExprTuple27
26Conditionalvalue: 28
condition: 31
27Lambdaparameters: 41
body: 29
28Operationoperator: 44
operands: 30
29Conditionalvalue: 33
condition: 31
30ExprTuple32, 33
31Operationoperator: 34
operands: 35
32Variable
33Operationoperator: 36
operands: 41
34Literal
35ExprTuple37, 38
36Variable
37ExprRangelambda_map: 39
start_index: 47
end_index: 48
38Operationoperator: 40
operands: 41
39Lambdaparameter: 54
body: 42
40Variable
41ExprTuple43
42Operationoperator: 44
operands: 45
43ExprRangelambda_map: 46
start_index: 47
end_index: 48
44Literal
45ExprTuple50, 49
46Lambdaparameter: 54
body: 50
47Literal
48Variable
49IndexedVarvariable: 51
index: 54
50IndexedVarvariable: 52
index: 54
51Variable
52Variable
53ExprTuple54
54Variable