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, InSet
from proveit.numbers import DecimalSequence, Digits, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
sub_expr3 = IndexedVar(c, sub_expr1)
sub_expr4 = IndexedVar(d, sub_expr1)
sub_expr5 = ExprRange(sub_expr1, b, one, n)
sub_expr6 = ExprRange(sub_expr1, sub_expr2, one, m)
sub_expr7 = ExprRange(sub_expr1, sub_expr3, one, n)
sub_expr8 = ExprRange(sub_expr1, sub_expr4, one, k)
expr = Lambda([sub_expr6, b, sub_expr7, sub_expr8], Conditional(Equals(DecimalSequence(sub_expr6, sub_expr5, sub_expr8), DecimalSequence(sub_expr6, sub_expr7, sub_expr8)), And(ExprRange(sub_expr1, InSet(sub_expr2, Digits), one, m), InSet(b, Digits), ExprRange(sub_expr1, InSet(sub_expr3, Digits), one, n), ExprRange(sub_expr1, InSet(sub_expr4, Digits), one, k), Equals([sub_expr5], [sub_expr7]))))

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, c_{1}, c_{2}, \ldots, c_{n}, d_{1}, d_{2}, \ldots, d_{k}\right) \mapsto \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}) \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}, \left(c_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(c_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(c_{n} \in \mathbb{N}^{\leq 9}\right), \left(d_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(d_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(d_{k} \in \mathbb{N}^{\leq 9}\right) ,  \left(b, b, ..\left(n - 3\right) \times.., b\right) = \left(c_{1}, c_{2}, \ldots, c_{n}\right)\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	24, 50, 40, 25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 22 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12, 13, 14
8	Operation	operator: 16 operands: 15
9	Operation	operator: 16 operands: 17
10	ExprRange	lambda_map: 18 start_index: 46 end_index: 32
11	Operation	operator: 37 operands: 19
12	ExprRange	lambda_map: 20 start_index: 46 end_index: 47
13	ExprRange	lambda_map: 21 start_index: 46 end_index: 34
14	Operation	operator: 22 operands: 23
15	ExprTuple	24, 39, 25
16	Literal
17	ExprTuple	24, 40, 25
18	Lambda	parameter: 54 body: 26
19	ExprTuple	50, 43
20	Lambda	parameter: 54 body: 27
21	Lambda	parameter: 54 body: 28
22	Literal
23	ExprTuple	29, 30
24	ExprRange	lambda_map: 31 start_index: 46 end_index: 32
25	ExprRange	lambda_map: 33 start_index: 46 end_index: 34
26	Operation	operator: 37 operands: 35
27	Operation	operator: 37 operands: 36
28	Operation	operator: 37 operands: 38
29	ExprTuple	39
30	ExprTuple	40
31	Lambda	parameter: 54 body: 41
32	Variable
33	Lambda	parameter: 54 body: 42
34	Variable
35	ExprTuple	41, 43
36	ExprTuple	51, 43
37	Literal
38	ExprTuple	42, 43
39	ExprRange	lambda_map: 44 start_index: 46 end_index: 47
40	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
41	IndexedVar	variable: 48 index: 54
42	IndexedVar	variable: 49 index: 54
43	Literal
44	Lambda	parameter: 54 body: 50
45	Lambda	parameter: 54 body: 51
46	Literal
47	Variable
48	Variable
49	Variable
50	Variable
51	IndexedVar	variable: 52 index: 54
52	Variable
53	ExprTuple	54
54	Variable