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Expression of type ExprTuple

from the theory of proveit.logic.sets.intersection

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, ExprRange, ExprTuple, IndexedVar, Lambda, S, Variable, n, y
from proveit.core_expr_types import Q__y_1_to_n, y_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([y_1_to_n], Conditional(Q__y_1_to_n, And(ExprRange(sub_expr1, InSet(IndexedVar(y, sub_expr1), IndexedVar(S, sub_expr1)), one, 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(\left(y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{Q\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } \left(y_{1} \in S_{1}\right) \land  \left(y_{2} \in S_{2}\right) \land  \ldots \land  \left(y_{n} \in S_{n}\right)\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
1Lambdaparameters: 6
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Variable
6ExprTuple9
7Literal
8ExprTuple10
9ExprRangelambda_map: 11
start_index: 13
end_index: 14
10ExprRangelambda_map: 12
start_index: 13
end_index: 14
11Lambdaparameter: 23
body: 18
12Lambdaparameter: 23
body: 15
13Literal
14Variable
15Operationoperator: 16
operands: 17
16Literal
17ExprTuple18, 19
18IndexedVarvariable: 20
index: 23
19IndexedVarvariable: 21
index: 23
20Variable
21Variable
22ExprTuple23
23Variable