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, b, c, d, k, m, n
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = ExprRange(sub_expr1, b, one, n)
sub_expr3 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, m)
sub_expr4 = ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, n)
sub_expr5 = ExprRange(sub_expr1, IndexedVar(d, sub_expr1), one, k)
expr = Lambda([m, n, k], Conditional(Forall(instance_param_or_params = [sub_expr3, b, sub_expr4, sub_expr5], instance_expr = Equals(DecimalSequence(sub_expr3, sub_expr2, sub_expr5), DecimalSequence(sub_expr3, sub_expr4, sub_expr5)), domain = Digits, condition = Equals([sub_expr2], [sub_expr4])), 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, c_{1}, c_{2}, \ldots, c_{n}, d_{1}, d_{2}, \ldots, d_{k} \in \mathbb{N}^{\leq 9}~|~\left(b, b, ..\left(n - 3\right) \times.., b\right) = \left(c_{1}, c_{2}, \ldots, c_{n}\right)}~\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ b, b, ..\left(n - 3\right) \times.., b ~ d_{1}, d_{2}, \ldots, d_{k}) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ c_{1}, c_{2}, \ldots, c_{n} ~ 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, 62, 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, 65, 55, 40
13	Conditional	value: 17 condition: 18
14	ExprTuple	47, 19
15	ExprTuple	62, 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: 61 end_index: 47
26	Operation	operator: 52 operands: 34
27	ExprRange	lambda_map: 35 start_index: 61 end_index: 62
28	ExprRange	lambda_map: 36 start_index: 61 end_index: 49
29	Operation	operator: 37 operands: 38
30	ExprTuple	39, 54, 40
31	Literal
32	ExprTuple	39, 55, 40
33	Lambda	parameter: 69 body: 41
34	ExprTuple	65, 58
35	Lambda	parameter: 69 body: 42
36	Lambda	parameter: 69 body: 43
37	Literal
38	ExprTuple	44, 45
39	ExprRange	lambda_map: 46 start_index: 61 end_index: 47
40	ExprRange	lambda_map: 48 start_index: 61 end_index: 49
41	Operation	operator: 52 operands: 50
42	Operation	operator: 52 operands: 51
43	Operation	operator: 52 operands: 53
44	ExprTuple	54
45	ExprTuple	55
46	Lambda	parameter: 69 body: 56
47	Variable
48	Lambda	parameter: 69 body: 57
49	Variable
50	ExprTuple	56, 58
51	ExprTuple	66, 58
52	Literal
53	ExprTuple	57, 58
54	ExprRange	lambda_map: 59 start_index: 61 end_index: 62
55	ExprRange	lambda_map: 60 start_index: 61 end_index: 62
56	IndexedVar	variable: 63 index: 69
57	IndexedVar	variable: 64 index: 69
58	Literal
59	Lambda	parameter: 69 body: 65
60	Lambda	parameter: 69 body: 66
61	Literal
62	Variable
63	Variable
64	Variable
65	Variable
66	IndexedVar	variable: 67 index: 69
67	Variable
68	ExprTuple	69
69	Variable