# 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, ExprTuple, 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 = ExprTuple(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(\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..\right)

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple33, 34, 35, 36
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 22
operands: 8
6Literal
7ExprTuple9, 10
8ExprTuple11, 12, 13, 14, 15
9Operationoperator: 16
operands: 28
10Operationoperator: 16
operands: 32
11Operationoperator: 20
operands: 17
12Operationoperator: 20
operands: 18
13Operationoperator: 20
operands: 19
14Operationoperator: 20
operands: 21
15Operationoperator: 22
operands: 23
16Literal
17ExprTuple33, 24
18ExprTuple34, 24
19ExprTuple35, 24
20Literal
21ExprTuple36, 24
22Literal
23ExprTuple25, 26, 27
24Literal
25Operationoperator: 31
operands: 28
26Operationoperator: 29
operands: 30
27Operationoperator: 31
operands: 32
28ExprTuple33, 34
29Literal
30ExprTuple34, 35
31Literal
32ExprTuple35, 36
33Variable
34Variable
35Variable
36Variable