Expression of type Lambda

from the theory of proveit.linear_algebra.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, K, Lambda, V, c, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.linear_algebra import VecAdd, VecSpaces
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [i, j, k], instance_expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c, d_1_to_k], instance_expr = Equals(VecAdd(a_1_to_i, b_1_to_j, c, d_1_to_k), VecAdd(a_1_to_i, c, b_1_to_j, d_1_to_k)).with_wrapping_at(2), domain = V), domain = Natural), InClass(V, VecSpaces(K))))

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())

V \mapsto \left\{\forall_{i, j, k \in \mathbb{N}}~\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 V}~\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)\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 69 body: 2
1	ExprTuple	69
2	Conditional	value: 3 condition: 4
3	Operation	operator: 17 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	69, 9
8	Lambda	parameters: 10 body: 11
9	Operation	operator: 12 operand: 16
10	ExprTuple	56, 58, 61
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operand: 20
15	Operation	operator: 33 operands: 19
16	Variable
17	Literal
18	ExprTuple	20
19	ExprTuple	21, 22, 23
20	Lambda	parameters: 41 body: 24
21	Operation	operator: 64 operands: 25
22	Operation	operator: 64 operands: 26
23	Operation	operator: 64 operands: 27
24	Conditional	value: 28 condition: 29
25	ExprTuple	56, 30
26	ExprTuple	58, 30
27	ExprTuple	61, 30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	Literal
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37, 38, 39, 40
35	Operation	operator: 42 operands: 41
36	Operation	operator: 42 operands: 43
37	ExprRange	lambda_map: 44 start_index: 60 end_index: 56
38	ExprRange	lambda_map: 45 start_index: 60 end_index: 58
39	Operation	operator: 64 operands: 46
40	ExprRange	lambda_map: 47 start_index: 60 end_index: 61
41	ExprTuple	48, 49, 53, 50
42	Literal
43	ExprTuple	48, 53, 49, 50
44	Lambda	parameter: 74 body: 51
45	Lambda	parameter: 74 body: 52
46	ExprTuple	53, 69
47	Lambda	parameter: 74 body: 54
48	ExprRange	lambda_map: 55 start_index: 60 end_index: 56
49	ExprRange	lambda_map: 57 start_index: 60 end_index: 58
50	ExprRange	lambda_map: 59 start_index: 60 end_index: 61
51	Operation	operator: 64 operands: 62
52	Operation	operator: 64 operands: 63
53	Variable
54	Operation	operator: 64 operands: 65
55	Lambda	parameter: 74 body: 66
56	Variable
57	Lambda	parameter: 74 body: 67
58	Variable
59	Lambda	parameter: 74 body: 68
60	Literal
61	Variable
62	ExprTuple	66, 69
63	ExprTuple	67, 69
64	Literal
65	ExprTuple	68, 69
66	IndexedVar	variable: 70 index: 74
67	IndexedVar	variable: 71 index: 74
68	IndexedVar	variable: 72 index: 74
69	Variable
70	Variable
71	Variable
72	Variable
73	ExprTuple	74
74	Variable