Expression of type Conditional

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, 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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