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Expression of type Conditional

from the theory of proveit.numbers.number_sets.integers

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, a, b, x
from proveit.logic import And, InSet, NotInSet, Or
from proveit.numbers import Integer, Interval, Less
In [2]:
# build up the expression from sub-expressions
expr = Conditional(NotInSet(x, Interval(a, b)), And(InSet(a, Integer), InSet(b, Integer), InSet(x, Integer), Or(Less(x, a), Less(b, x))))
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 \notin \{a~\ldotp \ldotp~b\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  x \in \mathbb{Z} ,  \left(x < a\right) \lor \left(b < x\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: 5
operands: 6
3Literal
4ExprTuple28, 7
5Literal
6ExprTuple8, 9, 10, 11
7Operationoperator: 12
operands: 13
8Operationoperator: 16
operands: 14
9Operationoperator: 16
operands: 15
10Operationoperator: 16
operands: 17
11Operationoperator: 18
operands: 19
12Literal
13ExprTuple26, 27
14ExprTuple26, 20
15ExprTuple27, 20
16Literal
17ExprTuple28, 20
18Literal
19ExprTuple21, 22
20Literal
21Operationoperator: 24
operands: 23
22Operationoperator: 24
operands: 25
23ExprTuple28, 26
24Literal
25ExprTuple27, 28
26Variable
27Variable
28Variable