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, ExprRange, IndexedVar, Variable, a, b, c, d, e, 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, InSet
from proveit.numbers import Add, Complex, Neg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Add(a_1_to_i, Neg(b), c_1_to_j, d, e_1_to_k), Add(a_1_to_i, c_1_to_j, e_1_to_k)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), InSet(b, Complex), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Complex), one, j), InSet(d, Complex), ExprRange(sub_expr1, InSet(IndexedVar(e, sub_expr1), Complex), one, 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())

\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) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right) ,  b \in \mathbb{C}, \left(c_{1} \in \mathbb{C}\right) ,  \left(c_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(c_{j} \in \mathbb{C}\right) ,  d \in \mathbb{C}, \left(e_{1} \in \mathbb{C}\right) ,  \left(e_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(e_{k} \in \mathbb{C}\right)\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11, 12, 13
7	Operation	operator: 15 operands: 14
8	Operation	operator: 15 operands: 16
9	ExprRange	lambda_map: 17 start_index: 37 end_index: 33
10	Operation	operator: 41 operands: 18
11	ExprRange	lambda_map: 19 start_index: 37 end_index: 35
12	Operation	operator: 41 operands: 20
13	ExprRange	lambda_map: 21 start_index: 37 end_index: 38
14	ExprTuple	23, 22, 24, 28, 25
15	Literal
16	ExprTuple	23, 24, 25
17	Lambda	parameter: 52 body: 26
18	ExprTuple	43, 47
19	Lambda	parameter: 52 body: 27
20	ExprTuple	28, 47
21	Lambda	parameter: 52 body: 29
22	Operation	operator: 30 operand: 43
23	ExprRange	lambda_map: 32 start_index: 37 end_index: 33
24	ExprRange	lambda_map: 34 start_index: 37 end_index: 35
25	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
26	Operation	operator: 41 operands: 39
27	Operation	operator: 41 operands: 40
28	Variable
29	Operation	operator: 41 operands: 42
30	Literal
31	ExprTuple	43
32	Lambda	parameter: 52 body: 44
33	Variable
34	Lambda	parameter: 52 body: 45
35	Variable
36	Lambda	parameter: 52 body: 46
37	Literal
38	Variable
39	ExprTuple	44, 47
40	ExprTuple	45, 47
41	Literal
42	ExprTuple	46, 47
43	Variable
44	IndexedVar	variable: 48 index: 52
45	IndexedVar	variable: 49 index: 52
46	IndexedVar	variable: 50 index: 52
47	Literal
48	Variable
49	Variable
50	Variable
51	ExprTuple	52
52	Variable