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Expression of type Conditional

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, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import InSet, Intersect
from proveit.logic.sets import x_in_every_A
In [2]:
# build up the expression from sub-expressions
expr = Conditional(x_in_every_A, InSet(x, Intersect(A_1_to_m)))
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(x \in A_{1}\right) \land  \left(x \in A_{2}\right) \land  \ldots \land  \left(x \in A_{m}\right) \textrm{ if } x \in \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\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: 4
2Operationoperator: 13
operands: 5
3Literal
4ExprTuple6
5ExprTuple18, 7
6ExprRangelambda_map: 8
start_index: 16
end_index: 17
7Operationoperator: 9
operands: 10
8Lambdaparameter: 22
body: 11
9Literal
10ExprTuple12
11Operationoperator: 13
operands: 14
12ExprRangelambda_map: 15
start_index: 16
end_index: 17
13Literal
14ExprTuple18, 19
15Lambdaparameter: 22
body: 19
16Literal
17Variable
18Variable
19IndexedVarvariable: 20
index: 22
20Variable
21ExprTuple22
22Variable