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Expression of type Conditional

from the theory of proveit.logic.sets.subtraction

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, S, x, y
from proveit.logic import And, Difference, InSet, NotEquals, Set
In [2]:
# build up the expression from sub-expressions
expr = Conditional(InSet(x, Difference(S, Set(y))), And(InSet(x, S), NotEquals(x, y)))
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\{x \in \left(S - \left\{y\right\}\right) \textrm{ if } x \in S ,  x \neq y\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: 11
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple17, 6
4Literal
5ExprTuple7, 8
6Operationoperator: 9
operands: 10
7Operationoperator: 11
operands: 12
8Operationoperator: 13
operands: 14
9Literal
10ExprTuple16, 15
11Literal
12ExprTuple17, 16
13Literal
14ExprTuple17, 20
15Operationoperator: 18
operand: 20
16Variable
17Variable
18Literal
19ExprTuple20
20Variable