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Expression of type Lambda

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, Lambda, 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 = Lambda(n, 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())
n \mapsto \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()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 21
body: 2
1ExprTuple21
2Conditionalvalue: 3
condition: 4
3Operationoperator: 10
operands: 5
4Operationoperator: 12
operands: 6
5ExprTuple21, 7
6ExprTuple8, 9
7Literal
8Operationoperator: 10
operands: 11
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple21, 14
12Literal
13ExprTuple15, 16
14Literal
15Operationoperator: 18
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 21
18Literal
19ExprTuple21, 22
20Literal
21Variable
22Literal