# 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, InSet
from proveit.numbers import Integer, Less, LessEq

In [2]:
# build up the expression from sub-expressions
expr = 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 \in \mathbb{Z}\right) \land \left(b \in \mathbb{Z}\right) \land \left(c \in \mathbb{Z}\right) \land \left(d \in \mathbb{Z}\right) \land \left(a \leq b < c \leq d\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 12
operands: 1
1ExprTuple2, 3, 4, 5, 6
2Operationoperator: 10
operands: 7
3Operationoperator: 10
operands: 8
4Operationoperator: 10
operands: 9
5Operationoperator: 10
operands: 11
6Operationoperator: 12
operands: 13
7ExprTuple23, 14
8ExprTuple24, 14
9ExprTuple25, 14
10Literal
11ExprTuple26, 14
12Literal
13ExprTuple15, 16, 17
14Literal
15Operationoperator: 21
operands: 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18ExprTuple23, 24
19Literal
20ExprTuple24, 25
21Literal
22ExprTuple25, 26
23Variable
24Variable
25Variable
26Variable