# 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.
# import Expression classes needed to build the expression
from proveit import n
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Digits, LessEq, Natural, nine

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Equals(InSet(n, Digits), And(InSet(n, Natural), LessEq(n, nine))))

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_{n}~\left(\left(n \in \mathbb{N}^{\leq 9}\right) = \left(\left(n \in \mathbb{N}\right) \land \left(n \leq 9\right)\right)\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
3Lambdaparameter: 21
body: 5
4ExprTuple21
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Operationoperator: 16
operands: 10
9Operationoperator: 11
operands: 12
10ExprTuple21, 13
11Literal
12ExprTuple14, 15
13Literal
14Operationoperator: 16
operands: 17
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple21, 20
18Literal
19ExprTuple21, 22
20Literal
21Variable
22Literal