Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	48, 63, 50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 22 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 13 body: 14
10	Operation	operator: 53 operands: 15
11	Operation	operator: 53 operands: 16
12	Operation	operator: 53 operands: 17
13	ExprTuple	40, 66, 56, 41
14	Conditional	value: 18 condition: 19
15	ExprTuple	48, 20
16	ExprTuple	63, 20
17	ExprTuple	50, 20
18	Operation	operator: 38 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27, 28, 29, 30
24	Operation	operator: 32 operands: 31
25	Operation	operator: 32 operands: 33
26	ExprRange	lambda_map: 34 start_index: 62 end_index: 48
27	Operation	operator: 53 operands: 35
28	ExprRange	lambda_map: 36 start_index: 62 end_index: 63
29	ExprRange	lambda_map: 37 start_index: 62 end_index: 50
30	Operation	operator: 38 operands: 39
31	ExprTuple	40, 55, 41
32	Literal
33	ExprTuple	40, 56, 41
34	Lambda	parameter: 70 body: 42
35	ExprTuple	66, 59
36	Lambda	parameter: 70 body: 43
37	Lambda	parameter: 70 body: 44
38	Literal
39	ExprTuple	45, 46
40	ExprRange	lambda_map: 47 start_index: 62 end_index: 48
41	ExprRange	lambda_map: 49 start_index: 62 end_index: 50
42	Operation	operator: 53 operands: 51
43	Operation	operator: 53 operands: 52
44	Operation	operator: 53 operands: 54
45	ExprTuple	55
46	ExprTuple	56
47	Lambda	parameter: 70 body: 57
48	Variable
49	Lambda	parameter: 70 body: 58
50	Variable
51	ExprTuple	57, 59
52	ExprTuple	67, 59
53	Literal
54	ExprTuple	58, 59
55	ExprRange	lambda_map: 60 start_index: 62 end_index: 63
56	ExprRange	lambda_map: 61 start_index: 62 end_index: 63
57	IndexedVar	variable: 64 index: 70
58	IndexedVar	variable: 65 index: 70
59	Literal
60	Lambda	parameter: 70 body: 66
61	Lambda	parameter: 70 body: 67
62	Literal
63	Variable
64	Variable
65	Variable
66	Variable
67	IndexedVar	variable: 68 index: 70
68	Variable
69	ExprTuple	70
70	Variable