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.core_expr_types import b_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, 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(d, sub_expr1)
sub_expr4 = ExprRange(sub_expr1, sub_expr2, one, m)
sub_expr5 = ExprRange(sub_expr1, sub_expr3, one, k)
sub_expr6 = Add(b_1_to_n)
expr = Lambda([sub_expr4, b_1_to_n, c, sub_expr5], Conditional(Equals(DecimalSequence(sub_expr4, sub_expr6, sub_expr5), DecimalSequence(sub_expr4, c, sub_expr5)), And(ExprRange(sub_expr1, InSet(sub_expr2, Digits), one, m), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Digits), one, n), InSet(c, Digits), ExprRange(sub_expr1, InSet(sub_expr3, Digits), one, k), Equals(sub_expr6, c))))

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_{1}, b_{2}, \ldots, b_{n}, c, d_{1}, d_{2}, \ldots, d_{k}\right) \mapsto \left\{\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ \left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) ~ d_{1}, d_{2}, \ldots, d_{k}) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ c ~ 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), \left(b_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(b_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(b_{n} \in \mathbb{N}^{\leq 9}\right) ,  c \in \mathbb{N}^{\leq 9}, \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_{1} +  b_{2} +  \ldots +  b_{n}\right) = c\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, 44, 30, 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: 48 end_index: 32
11	ExprRange	lambda_map: 19 start_index: 48 end_index: 49
12	Operation	operator: 37 operands: 20
13	ExprRange	lambda_map: 21 start_index: 48 end_index: 34
14	Operation	operator: 22 operands: 23
15	ExprTuple	24, 29, 25
16	Literal
17	ExprTuple	24, 30, 25
18	Lambda	parameter: 53 body: 26
19	Lambda	parameter: 53 body: 27
20	ExprTuple	30, 43
21	Lambda	parameter: 53 body: 28
22	Literal
23	ExprTuple	29, 30
24	ExprRange	lambda_map: 31 start_index: 48 end_index: 32
25	ExprRange	lambda_map: 33 start_index: 48 end_index: 34
26	Operation	operator: 37 operands: 35
27	Operation	operator: 37 operands: 36
28	Operation	operator: 37 operands: 38
29	Operation	operator: 39 operands: 40
30	Variable
31	Lambda	parameter: 53 body: 41
32	Variable
33	Lambda	parameter: 53 body: 42
34	Variable
35	ExprTuple	41, 43
36	ExprTuple	50, 43
37	Literal
38	ExprTuple	42, 43
39	Literal
40	ExprTuple	44
41	IndexedVar	variable: 45 index: 53
42	IndexedVar	variable: 46 index: 53
43	Literal
44	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
45	Variable
46	Variable
47	Lambda	parameter: 53 body: 50
48	Literal
49	Variable
50	IndexedVar	variable: 51 index: 53
51	Variable
52	ExprTuple	53
53	Variable