Expression of type Conditional

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, 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 = 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\{\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()

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: 27 body: 10
7	Operation	operator: 50 operands: 11
8	Operation	operator: 50 operands: 12
9	Operation	operator: 50 operands: 13
10	Conditional	value: 14 condition: 15
11	ExprTuple	42, 16
12	ExprTuple	44, 16
13	ExprTuple	47, 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, 26
21	Operation	operator: 28 operands: 27
22	Operation	operator: 28 operands: 29
23	ExprRange	lambda_map: 30 start_index: 46 end_index: 42
24	ExprRange	lambda_map: 31 start_index: 46 end_index: 44
25	Operation	operator: 50 operands: 32
26	ExprRange	lambda_map: 33 start_index: 46 end_index: 47
27	ExprTuple	34, 35, 39, 36
28	Literal
29	ExprTuple	34, 39, 35, 36
30	Lambda	parameter: 60 body: 37
31	Lambda	parameter: 60 body: 38
32	ExprTuple	39, 55
33	Lambda	parameter: 60 body: 40
34	ExprRange	lambda_map: 41 start_index: 46 end_index: 42
35	ExprRange	lambda_map: 43 start_index: 46 end_index: 44
36	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
37	Operation	operator: 50 operands: 48
38	Operation	operator: 50 operands: 49
39	Variable
40	Operation	operator: 50 operands: 51
41	Lambda	parameter: 60 body: 52
42	Variable
43	Lambda	parameter: 60 body: 53
44	Variable
45	Lambda	parameter: 60 body: 54
46	Literal
47	Variable
48	ExprTuple	52, 55
49	ExprTuple	53, 55
50	Literal
51	ExprTuple	54, 55
52	IndexedVar	variable: 56 index: 60
53	IndexedVar	variable: 57 index: 60
54	IndexedVar	variable: 58 index: 60
55	Literal
56	Variable
57	Variable
58	Variable
59	ExprTuple	60
60	Variable