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, ExprRange, IndexedVar, Lambda, Variable, a, c, d, k, m, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, DecimalSequence, Digits, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, m)
sub_expr3 = ExprRange(sub_expr1, IndexedVar(d, sub_expr1), one, k)
sub_expr4 = Add(b_1_to_n)
expr = Lambda([m, n, k], Conditional(Forall(instance_param_or_params = [sub_expr2, b_1_to_n, c, sub_expr3], instance_expr = Equals(DecimalSequence(sub_expr2, sub_expr4, sub_expr3), DecimalSequence(sub_expr2, c, sub_expr3)), domain = Digits, condition = Equals(sub_expr4, c)), And(InSet(m, Natural), InSet(n, Natural), InSet(k, 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())

\left(m, n, k\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b_{1}, b_{2}, \ldots, b_{n}, c, d_{1}, d_{2}, \ldots, d_{k} \in \mathbb{N}^{\leq 9}~|~\left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) = c}~\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ \left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) ~ d_{1}, d_{2}, \ldots, d_{k}) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ c ~ d_{1}, d_{2}, \ldots, d_{k})\right) \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N} ,  k \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	parameters: 1 body: 2
1	ExprTuple	47, 64, 49
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 21 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 12 body: 13
9	Operation	operator: 52 operands: 14
10	Operation	operator: 52 operands: 15
11	Operation	operator: 52 operands: 16
12	ExprTuple	39, 59, 45, 40
13	Conditional	value: 17 condition: 18
14	ExprTuple	47, 19
15	ExprTuple	64, 19
16	ExprTuple	49, 19
17	Operation	operator: 37 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27, 28, 29
23	Operation	operator: 31 operands: 30
24	Operation	operator: 31 operands: 32
25	ExprRange	lambda_map: 33 start_index: 63 end_index: 47
26	ExprRange	lambda_map: 34 start_index: 63 end_index: 64
27	Operation	operator: 52 operands: 35
28	ExprRange	lambda_map: 36 start_index: 63 end_index: 49
29	Operation	operator: 37 operands: 38
30	ExprTuple	39, 44, 40
31	Literal
32	ExprTuple	39, 45, 40
33	Lambda	parameter: 68 body: 41
34	Lambda	parameter: 68 body: 42
35	ExprTuple	45, 58
36	Lambda	parameter: 68 body: 43
37	Literal
38	ExprTuple	44, 45
39	ExprRange	lambda_map: 46 start_index: 63 end_index: 47
40	ExprRange	lambda_map: 48 start_index: 63 end_index: 49
41	Operation	operator: 52 operands: 50
42	Operation	operator: 52 operands: 51
43	Operation	operator: 52 operands: 53
44	Operation	operator: 54 operands: 55
45	Variable
46	Lambda	parameter: 68 body: 56
47	Variable
48	Lambda	parameter: 68 body: 57
49	Variable
50	ExprTuple	56, 58
51	ExprTuple	65, 58
52	Literal
53	ExprTuple	57, 58
54	Literal
55	ExprTuple	59
56	IndexedVar	variable: 60 index: 68
57	IndexedVar	variable: 61 index: 68
58	Literal
59	ExprRange	lambda_map: 62 start_index: 63 end_index: 64
60	Variable
61	Variable
62	Lambda	parameter: 68 body: 65
63	Literal
64	Variable
65	IndexedVar	variable: 66 index: 68
66	Variable
67	ExprTuple	68
68	Variable