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, 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 = 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(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..

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	31, 33
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 26 operands: 14
10	Operation	operator: 24 operands: 15
11	ExprRange	lambda_map: 16 start_index: 39 end_index: 37
12	Operation	operator: 29 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	20, 39
15	ExprTuple	31, 21, 22
16	Lambda	parameter: 45 body: 23
17	ExprTuple	33, 35
18	Literal
19	ExprTuple	33, 42
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	ExprRange	lambda_map: 28 start_index: 39 end_index: 40
23	Operation	operator: 29 operands: 30
24	Literal
25	ExprTuple	31, 33, 32
26	Literal
27	ExprTuple	33, 39
28	Lambda	parameter: 45 body: 34
29	Literal
30	ExprTuple	41, 35
31	ExprRange	lambda_map: 36 start_index: 39 end_index: 37
32	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
33	Variable
34	Literal
35	Literal
36	Lambda	parameter: 45 body: 41
37	Variable
38	Lambda	parameter: 45 body: 42
39	Literal
40	Variable
41	IndexedVar	variable: 43 index: 45
42	Literal
43	Variable
44	ExprTuple	45
45	Variable