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, k, m
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, DecimalSequence, Digits, Less, nine, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
sub_expr3 = ExprRange(sub_expr1, sub_expr2, one, m)
expr = ExprTuple(Lambda([sub_expr3, b], Conditional(Equals(Add(DecimalSequence(sub_expr3, b, ExprRange(sub_expr1, nine, one, k)), one), DecimalSequence(sub_expr3, Add(b, one), ExprRange(sub_expr1, zero, one, k))), And(ExprRange(sub_expr1, InSet(sub_expr2, Digits), one, m), InSet(b, Digits), Less(b, nine)))))

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(a_{1}, a_{2}, \ldots, a_{m}, b\right) \mapsto \left\{\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ b ~ 9, 9, ..\left(k - 3\right) \times.., 9) + 1\right) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ \left(b + 1\right) ~ 0, 0, ..\left(k - 3\right) \times.., 0) \textrm{ if } \left(a_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(a_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(a_{m} \in \mathbb{N}^{\leq 9}\right) ,  b \in \mathbb{N}^{\leq 9} ,  b < 9\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	32, 34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 27 operands: 15
11	Operation	operator: 25 operands: 16
12	ExprRange	lambda_map: 17 start_index: 40 end_index: 38
13	Operation	operator: 30 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21, 40
16	ExprTuple	32, 22, 23
17	Lambda	parameter: 46 body: 24
18	ExprTuple	34, 36
19	Literal
20	ExprTuple	34, 43
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	ExprRange	lambda_map: 29 start_index: 40 end_index: 41
24	Operation	operator: 30 operands: 31
25	Literal
26	ExprTuple	32, 34, 33
27	Literal
28	ExprTuple	34, 40
29	Lambda	parameter: 46 body: 35
30	Literal
31	ExprTuple	42, 36
32	ExprRange	lambda_map: 37 start_index: 40 end_index: 38
33	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
34	Variable
35	Literal
36	Literal
37	Lambda	parameter: 46 body: 42
38	Variable
39	Lambda	parameter: 46 body: 43
40	Literal
41	Variable
42	IndexedVar	variable: 44 index: 46
43	Literal
44	Variable
45	ExprTuple	46
46	Variable