logo

Expression of type Conditional

from the theory of proveit.numbers.numerals.decimals

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, n
from proveit.logic import And, InSet
from proveit.numbers import Digits, LessEq, Natural, nine, zero
In [2]:
# build up the expression from sub-expressions
expr = Conditional(InSet(n, Digits), And(InSet(n, Natural), And(LessEq(zero, n), LessEq(n, nine)).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\{n \in \mathbb{N}^{\leq 9} \textrm{ if } n \in \mathbb{N} ,  0 \leq n \leq 9\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: 8
operands: 3
2Operationoperator: 10
operands: 4
3ExprTuple19, 5
4ExprTuple6, 7
5Literal
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple19, 12
10Literal
11ExprTuple13, 14
12Literal
13Operationoperator: 16
operands: 15
14Operationoperator: 16
operands: 17
15ExprTuple18, 19
16Literal
17ExprTuple19, 20
18Literal
19Variable
20Literal