# 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.
# import Expression classes needed to build the expression
from proveit import Conditional, a, b, c, d
from proveit.logic import And, InSet, SubsetEq
from proveit.numbers import Integer, Interval, LessEq
In [2]:
# build up the expression from sub-expressions
expr = Conditional(SubsetEq(Interval(b, c), Interval(a, d)), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), InSet(d, Integer), And(LessEq(a, b), LessEq(b, c), LessEq(c, d)).with_total_ordering_style()))
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\{\{b~\ldotp \ldotp~c\} \subseteq \{a~\ldotp \ldotp~d\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  d \in \mathbb{Z} ,  a \leq b \leq c \leq d\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: 20
operands: 5
3Literal
4ExprTuple6, 7
5ExprTuple8, 9, 10, 11, 12
6Operationoperator: 13
operands: 27
7Operationoperator: 13
operands: 14
8Operationoperator: 18
operands: 15
9Operationoperator: 18
operands: 16
10Operationoperator: 18
operands: 17
11Operationoperator: 18
operands: 19
12Operationoperator: 20
operands: 21
13Literal
14ExprTuple30, 33
15ExprTuple30, 22
16ExprTuple31, 22
17ExprTuple32, 22
18Literal
19ExprTuple33, 22
20Literal
21ExprTuple23, 24, 25
22Literal
23Operationoperator: 28
operands: 26
24Operationoperator: 28
operands: 27
25Operationoperator: 28
operands: 29
26ExprTuple30, 31
27ExprTuple31, 32
28Literal
29ExprTuple32, 33
30Variable
31Variable
32Variable
33Variable