Expression of type Lambda

from the theory of proveit.numbers.numerals.decimals

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.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(DecimalSequence(a_1_to_n), Natural), domain = Digits), InSet(n, NaturalPos)))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

n \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{N}^{\leq 9}}~\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{n}) \in \mathbb{N}\right) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 26 body: 2
1	ExprTuple	26
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 27 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	26, 9
8	Lambda	parameters: 20 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 27 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprRange	lambda_map: 21 start_index: 25 end_index: 26
19	Literal
20	ExprTuple	22
21	Lambda	parameter: 33 body: 23
22	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
23	Operation	operator: 27 operands: 28
24	Lambda	parameter: 33 body: 29
25	Literal
26	Variable
27	Literal
28	ExprTuple	29, 30
29	IndexedVar	variable: 31 index: 33
30	Literal
31	Variable
32	ExprTuple	33
33	Variable