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Expression of type Conditional

from the theory of proveit.logic.sets.comprehension

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, IndexedVar, S, Variable, n, x
from proveit.core_expr_types import R__x_1_to_n, f__x_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 = Conditional(f__x_1_to_n, And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), IndexedVar(S, sub_expr1)), one, n), R__x_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\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } \left(x_{1} \in S_{1}\right) ,  \left(x_{2} \in S_{2}\right) ,  \ldots ,  \left(x_{n} \in S_{n}\right) ,  R\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 10
2Operationoperator: 4
operands: 5
3Variable
4Literal
5ExprTuple6, 7
6ExprRangelambda_map: 8
start_index: 16
end_index: 17
7Operationoperator: 9
operands: 10
8Lambdaparameter: 23
body: 11
9Variable
10ExprTuple12
11Operationoperator: 13
operands: 14
12ExprRangelambda_map: 15
start_index: 16
end_index: 17
13Literal
14ExprTuple19, 18
15Lambdaparameter: 23
body: 19
16Literal
17Variable
18IndexedVarvariable: 20
index: 23
19IndexedVarvariable: 21
index: 23
20Variable
21Variable
22ExprTuple23
23Variable