# 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 ExprTuple, a, b, c, d
from proveit.logic import And, InSet
from proveit.numbers import Integer, LessEq

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(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(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
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2, 3, 4, 5
1Operationoperator: 9
operands: 6
2Operationoperator: 9
operands: 7
3Operationoperator: 9
operands: 8
4Operationoperator: 9
operands: 10
5Operationoperator: 11
operands: 12
6ExprTuple21, 13
7ExprTuple22, 13
8ExprTuple23, 13
9Literal
10ExprTuple24, 13
11Literal
12ExprTuple14, 15, 16
13Literal
14Operationoperator: 19
operands: 17
15Operationoperator: 19
operands: 18
16Operationoperator: 19
operands: 20
17ExprTuple21, 22
18ExprTuple22, 23
19Literal
20ExprTuple23, 24
21Variable
22Variable
23Variable
24Variable