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, 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(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..

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