# from the theory of proveit.numbers.ordering¶

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, a, b, c
from proveit.logic import And, InSet
from proveit.numbers import Add, Less, LessEq, Real, zero

In [2]:
# build up the expression from sub-expressions
expr = Conditional(Less(a, Add(b, c)), And(InSet(a, Real), InSet(b, Real), InSet(c, Real), LessEq(a, b), Less(zero, c)))

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 < \left(b + c\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  c \in \mathbb{R} ,  a \leq b ,  0 < c\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 20
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple23, 6
4Literal
5ExprTuple7, 8, 9, 10, 11
6Operationoperator: 12
operands: 13
7Operationoperator: 16
operands: 14
8Operationoperator: 16
operands: 15
9Operationoperator: 16
operands: 17
10Operationoperator: 18
operands: 19
11Operationoperator: 20
operands: 21
12Literal
13ExprTuple24, 26
14ExprTuple23, 22
15ExprTuple24, 22
16Literal
17ExprTuple26, 22
18Literal
19ExprTuple23, 24
20Literal
21ExprTuple25, 26
22Literal
23Variable
24Variable
25Literal
26Variable