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 K, Lambda, V, b, i, j, k
from proveit.core_expr_types import a_1_to_i, c_1_to_j, d_1_to_k
from proveit.linear_algebra import VecAdd, VecSpaces
from proveit.logic import Equals, Forall
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda(K, Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [i, j, k], instance_expr = Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j, d_1_to_k], instance_expr = Equals(VecAdd(a_1_to_i, b, c_1_to_j, d_1_to_k), VecAdd(a_1_to_i, c_1_to_j, b, d_1_to_k)).with_wrapping_at(2), domain = V), domain = Natural), domain = 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())

K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{i, j, k \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j}, 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+ c_{1} +  c_{2} +  \ldots +  c_{j}+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ c_{1} +  c_{2} +  \ldots +  c_{j} + b+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) \end{array} \end{array}\right)\right]\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: 19 body: 1
1	Operation	operator: 20 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 72 body: 5
4	ExprTuple	72
5	Conditional	value: 6 condition: 7
6	Operation	operator: 20 operand: 11
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	72, 12
11	Lambda	parameters: 13 body: 14
12	Operation	operator: 15 operand: 19
13	ExprTuple	59, 61, 64
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operand: 23
18	Operation	operator: 36 operands: 22
19	Variable
20	Literal
21	ExprTuple	23
22	ExprTuple	24, 25, 26
23	Lambda	parameters: 44 body: 27
24	Operation	operator: 67 operands: 28
25	Operation	operator: 67 operands: 29
26	Operation	operator: 67 operands: 30
27	Conditional	value: 31 condition: 32
28	ExprTuple	59, 33
29	ExprTuple	61, 33
30	ExprTuple	64, 33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Literal
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40, 41, 42, 43
38	Operation	operator: 45 operands: 44
39	Operation	operator: 45 operands: 46
40	ExprRange	lambda_map: 47 start_index: 63 end_index: 59
41	Operation	operator: 67 operands: 48
42	ExprRange	lambda_map: 49 start_index: 63 end_index: 61
43	ExprRange	lambda_map: 50 start_index: 63 end_index: 64
44	ExprTuple	51, 55, 52, 53
45	Literal
46	ExprTuple	51, 52, 55, 53
47	Lambda	parameter: 77 body: 54
48	ExprTuple	55, 72
49	Lambda	parameter: 77 body: 56
50	Lambda	parameter: 77 body: 57
51	ExprRange	lambda_map: 58 start_index: 63 end_index: 59
52	ExprRange	lambda_map: 60 start_index: 63 end_index: 61
53	ExprRange	lambda_map: 62 start_index: 63 end_index: 64
54	Operation	operator: 67 operands: 65
55	Variable
56	Operation	operator: 67 operands: 66
57	Operation	operator: 67 operands: 68
58	Lambda	parameter: 77 body: 69
59	Variable
60	Lambda	parameter: 77 body: 70
61	Variable
62	Lambda	parameter: 77 body: 71
63	Literal
64	Variable
65	ExprTuple	69, 72
66	ExprTuple	70, 72
67	Literal
68	ExprTuple	71, 72
69	IndexedVar	variable: 73 index: 77
70	IndexedVar	variable: 74 index: 77
71	IndexedVar	variable: 75 index: 77
72	Variable
73	Variable
74	Variable
75	Variable
76	ExprTuple	77
77	Variable