Expression of type Lambda

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, 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 = Lambda([a_1_to_i, b, c_1_to_j, d, e_1_to_k], 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(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)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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