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, a, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, NaturalPos, greater, zero

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a, b_1_to_n], instance_expr = InSet(DecimalSequence(a, b_1_to_n), NaturalPos), domain = Digits, condition = greater(a, zero)), InSet(n, Natural)))

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, b_{1}, b_{2}, \ldots, b_{n} \in \mathbb{N}^{\leq 9}~|~a > 0}~\left(\texttt{\#}(a ~ b_{1}, b_{2}, \ldots, b_{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: 33 body: 2
1	ExprTuple	33
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 34 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	33, 9
8	Lambda	parameters: 22 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 34 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19, 20
16	Operation	operator: 21 operands: 22
17	Literal
18	Operation	operator: 34 operands: 23
19	ExprRange	lambda_map: 24 start_index: 32 end_index: 33
20	Operation	operator: 25 operands: 26
21	Literal
22	ExprTuple	30, 27
23	ExprTuple	30, 37
24	Lambda	parameter: 40 body: 28
25	Literal
26	ExprTuple	29, 30
27	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
28	Operation	operator: 34 operands: 35
29	Literal
30	Variable
31	Lambda	parameter: 40 body: 36
32	Literal
33	Variable
34	Literal
35	ExprTuple	36, 37
36	IndexedVar	variable: 38 index: 40
37	Literal
38	Variable
39	ExprTuple	40
40	Variable