Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([a_1_to_i, b, c_1_to_j, d, e_1_to_k], Conditional(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)), 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), Equals(b, d)))))

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) \mapsto \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) ,  b = d\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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