Expression of type Conditional

from the theory of proveit.numbers.addition.subtraction

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, b, d, i, j, k
from proveit.core_expr_types import a_1_to_i, c_1_to_j, e_1_to_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Natural, Neg

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j, d, e_1_to_k], instance_expr = Equals(Add(a_1_to_i, b, c_1_to_j, Neg(d), e_1_to_k), Add(a_1_to_i, c_1_to_j, e_1_to_k)), domain = Complex, condition = Equals(b, d)), 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, c_{1}, c_{2}, \ldots, c_{j}, d, e_{1}, e_{2}, \ldots, e_{k} \in \mathbb{C}~|~b = d}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j} - d+ e_{1} +  e_{2} +  \ldots +  e_{k}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ c_{1} +  c_{2} +  \ldots +  c_{j}+ e_{1} +  e_{2} +  \ldots +  e_{k}\right)\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: 10 body: 11
7	Operation	operator: 58 operands: 12
8	Operation	operator: 58 operands: 13
9	Operation	operator: 58 operands: 14
10	ExprTuple	40, 46, 41, 60, 42
11	Conditional	value: 15 condition: 16
12	ExprTuple	50, 17
13	ExprTuple	52, 17
14	ExprTuple	55, 17
15	Operation	operator: 37 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24, 25, 26, 27, 28
21	Operation	operator: 30 operands: 29
22	Operation	operator: 30 operands: 31
23	ExprRange	lambda_map: 32 start_index: 54 end_index: 50
24	Operation	operator: 58 operands: 33
25	ExprRange	lambda_map: 34 start_index: 54 end_index: 52
26	Operation	operator: 58 operands: 35
27	ExprRange	lambda_map: 36 start_index: 54 end_index: 55
28	Operation	operator: 37 operands: 38
29	ExprTuple	40, 46, 41, 39, 42
30	Literal
31	ExprTuple	40, 41, 42
32	Lambda	parameter: 69 body: 43
33	ExprTuple	46, 64
34	Lambda	parameter: 69 body: 44
35	ExprTuple	60, 64
36	Lambda	parameter: 69 body: 45
37	Literal
38	ExprTuple	46, 60
39	Operation	operator: 47 operand: 60
40	ExprRange	lambda_map: 49 start_index: 54 end_index: 50
41	ExprRange	lambda_map: 51 start_index: 54 end_index: 52
42	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
43	Operation	operator: 58 operands: 56
44	Operation	operator: 58 operands: 57
45	Operation	operator: 58 operands: 59
46	Variable
47	Literal
48	ExprTuple	60
49	Lambda	parameter: 69 body: 61
50	Variable
51	Lambda	parameter: 69 body: 62
52	Variable
53	Lambda	parameter: 69 body: 63
54	Literal
55	Variable
56	ExprTuple	61, 64
57	ExprTuple	62, 64
58	Literal
59	ExprTuple	63, 64
60	Variable
61	IndexedVar	variable: 65 index: 69
62	IndexedVar	variable: 66 index: 69
63	IndexedVar	variable: 67 index: 69
64	Literal
65	Variable
66	Variable
67	Variable
68	ExprTuple	69
69	Variable