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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, ExprRange, IndexedVar, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(DecimalSequence(a_1_to_n), Natural), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Digits), one, n)))
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\{\texttt{\#}(a_{1}, a_{2}, \ldots, a_{n}) \in \mathbb{N} \textrm{ if } \left(a_{1} \in \mathbb{N}^{\leq 9}\right) \land  \left(a_{2} \in \mathbb{N}^{\leq 9}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{N}^{\leq 9}\right)\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: 17
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8
6Operationoperator: 9
operands: 10
7Literal
8ExprRangelambda_map: 11
start_index: 15
end_index: 16
9Literal
10ExprTuple12
11Lambdaparameter: 23
body: 13
12ExprRangelambda_map: 14
start_index: 15
end_index: 16
13Operationoperator: 17
operands: 18
14Lambdaparameter: 23
body: 19
15Literal
16Variable
17Literal
18ExprTuple19, 20
19IndexedVarvariable: 21
index: 23
20Literal
21Variable
22ExprTuple23
23Variable