Expression of type Lambda

from the theory of proveit.numbers.addition

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, Lambda, c, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Natural

# build up the expression from sub-expressions
expr = Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c, d_1_to_k], instance_expr = Equals(Add(a_1_to_i, b_1_to_j, c, d_1_to_k), Add(a_1_to_i, c, b_1_to_j, d_1_to_k)).with_wrapping_at(2), domain = Complex), And(InSet(i, Natural), InSet(j, 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(i, j, k\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c, d_{1}, d_{2}, \ldots, d_{k} \in \mathbb{C}}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j} + c+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i} + c+ b_{1} +  b_{2} +  \ldots +  b_{j}+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) \end{array} \end{array}\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\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	44, 46, 49
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 21 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 29 body: 12
9	Operation	operator: 52 operands: 13
10	Operation	operator: 52 operands: 14
11	Operation	operator: 52 operands: 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	44, 18
14	ExprTuple	46, 18
15	ExprTuple	49, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27, 28
23	Operation	operator: 30 operands: 29
24	Operation	operator: 30 operands: 31
25	ExprRange	lambda_map: 32 start_index: 48 end_index: 44
26	ExprRange	lambda_map: 33 start_index: 48 end_index: 46
27	Operation	operator: 52 operands: 34
28	ExprRange	lambda_map: 35 start_index: 48 end_index: 49
29	ExprTuple	36, 37, 41, 38
30	Literal
31	ExprTuple	36, 41, 37, 38
32	Lambda	parameter: 62 body: 39
33	Lambda	parameter: 62 body: 40
34	ExprTuple	41, 57
35	Lambda	parameter: 62 body: 42
36	ExprRange	lambda_map: 43 start_index: 48 end_index: 44
37	ExprRange	lambda_map: 45 start_index: 48 end_index: 46
38	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
39	Operation	operator: 52 operands: 50
40	Operation	operator: 52 operands: 51
41	Variable
42	Operation	operator: 52 operands: 53
43	Lambda	parameter: 62 body: 54
44	Variable
45	Lambda	parameter: 62 body: 55
46	Variable
47	Lambda	parameter: 62 body: 56
48	Literal
49	Variable
50	ExprTuple	54, 57
51	ExprTuple	55, 57
52	Literal
53	ExprTuple	56, 57
54	IndexedVar	variable: 58 index: 62
55	IndexedVar	variable: 59 index: 62
56	IndexedVar	variable: 60 index: 62
57	Literal
58	Variable
59	Variable
60	Variable
61	ExprTuple	62
62	Variable