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, Lambda, V, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.linear_algebra import VecAdd
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import 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_1_to_k], instance_expr = Equals(VecAdd(a_1_to_i, b_1_to_j, c_1_to_k), VecAdd(a_1_to_i, VecAdd(b_1_to_j), c_1_to_k)).with_wrapping_at(2), domain = V), 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_{1}, c_{2}, \ldots, c_{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_{1} +  c_{2} +  \ldots +  c_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right)+ c_{1} +  c_{2} +  \ldots +  c_{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	40, 55, 44
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: 28 body: 12
9	Operation	operator: 47 operands: 13
10	Operation	operator: 47 operands: 14
11	Operation	operator: 47 operands: 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	40, 18
14	ExprTuple	55, 18
15	ExprTuple	44, 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
23	Operation	operator: 41 operands: 28
24	Operation	operator: 41 operands: 29
25	ExprRange	lambda_map: 30 start_index: 54 end_index: 40
26	ExprRange	lambda_map: 31 start_index: 54 end_index: 55
27	ExprRange	lambda_map: 32 start_index: 54 end_index: 44
28	ExprTuple	33, 49, 35
29	ExprTuple	33, 34, 35
30	Lambda	parameter: 61 body: 36
31	Lambda	parameter: 61 body: 37
32	Lambda	parameter: 61 body: 38
33	ExprRange	lambda_map: 39 start_index: 54 end_index: 40
34	Operation	operator: 41 operands: 42
35	ExprRange	lambda_map: 43 start_index: 54 end_index: 44
36	Operation	operator: 47 operands: 45
37	Operation	operator: 47 operands: 46
38	Operation	operator: 47 operands: 48
39	Lambda	parameter: 61 body: 50
40	Variable
41	Literal
42	ExprTuple	49
43	Lambda	parameter: 61 body: 51
44	Variable
45	ExprTuple	50, 52
46	ExprTuple	58, 52
47	Literal
48	ExprTuple	51, 52
49	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
50	IndexedVar	variable: 56 index: 61
51	IndexedVar	variable: 57 index: 61
52	Variable
53	Lambda	parameter: 61 body: 58
54	Literal
55	Variable
56	Variable
57	Variable
58	IndexedVar	variable: 59 index: 61
59	Variable
60	ExprTuple	61
61	Variable