# 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, Lambda, a, b, c, d
from proveit.logic import And, Disjoint, InSet
from proveit.numbers import Integer, Interval, Less, LessEq

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b, c, d], Conditional(Disjoint(Interval(a, b), Interval(c, d)), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), InSet(d, Integer), And(LessEq(a, b), Less(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(a, b, c, d\right) \mapsto \left\{\textrm{disjoint}\left(\{a~\ldotp \ldotp~b\}, \{c~\ldotp \ldotp~d\}\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  d \in \mathbb{Z} ,  a \leq b < c \leq d\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple32, 33, 34, 35
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 21
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple10, 11, 12, 13, 14
8Operationoperator: 15
operands: 27
9Operationoperator: 15
operands: 31
10Operationoperator: 19
operands: 16
11Operationoperator: 19
operands: 17
12Operationoperator: 19
operands: 18
13Operationoperator: 19
operands: 20
14Operationoperator: 21
operands: 22
15Literal
16ExprTuple32, 23
17ExprTuple33, 23
18ExprTuple34, 23
19Literal
20ExprTuple35, 23
21Literal
22ExprTuple24, 25, 26
23Literal
24Operationoperator: 30
operands: 27
25Operationoperator: 28
operands: 29
26Operationoperator: 30
operands: 31
27ExprTuple32, 33
28Literal
29ExprTuple33, 34
30Literal
31ExprTuple34, 35
32Variable
33Variable
34Variable
35Variable