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

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c, d], instance_expr = Disjoint(Interval(a, b), Interval(c, d)), domain = Integer, condition = 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())

\forall_{a, b, c, d \in \mathbb{Z}~|~a \leq b < c \leq d}~\textrm{disjoint}\left(\{a~\ldotp \ldotp~b\}, \{c~\ldotp \ldotp~d\}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple35, 36, 37, 38
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 24
operands: 10
8Literal
9ExprTuple11, 12
10ExprTuple13, 14, 15, 16, 17
11Operationoperator: 18
operands: 30
12Operationoperator: 18
operands: 34
13Operationoperator: 22
operands: 19
14Operationoperator: 22
operands: 20
15Operationoperator: 22
operands: 21
16Operationoperator: 22
operands: 23
17Operationoperator: 24
operands: 25
18Literal
19ExprTuple35, 26
20ExprTuple36, 26
21ExprTuple37, 26
22Literal
23ExprTuple38, 26
24Literal
25ExprTuple27, 28, 29
26Literal
27Operationoperator: 33
operands: 30
28Operationoperator: 31
operands: 32
29Operationoperator: 33
operands: 34
30ExprTuple35, 36
31Literal
32ExprTuple36, 37
33Literal
34ExprTuple37, 38
35Variable
36Variable
37Variable
38Variable