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, Lambda, 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 = Lambda([i, j, k], 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, Neg(b), c_1_to_j, d, e_1_to_k), Add(a_1_to_i, c_1_to_j, e_1_to_k)), domain = Complex), 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(i, j, k\right) \mapsto \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}}~\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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	50, 52, 55
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 22 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 12 body: 13
9	Operation	operator: 58 operands: 14
10	Operation	operator: 58 operands: 15
11	Operation	operator: 58 operands: 16
12	ExprTuple	40, 60, 41, 45, 42
13	Conditional	value: 17 condition: 18
14	ExprTuple	50, 19
15	ExprTuple	52, 19
16	ExprTuple	55, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27, 28, 29, 30
24	Operation	operator: 32 operands: 31
25	Operation	operator: 32 operands: 33
26	ExprRange	lambda_map: 34 start_index: 54 end_index: 50
27	Operation	operator: 58 operands: 35
28	ExprRange	lambda_map: 36 start_index: 54 end_index: 52
29	Operation	operator: 58 operands: 37
30	ExprRange	lambda_map: 38 start_index: 54 end_index: 55
31	ExprTuple	40, 39, 41, 45, 42
32	Literal
33	ExprTuple	40, 41, 42
34	Lambda	parameter: 69 body: 43
35	ExprTuple	60, 64
36	Lambda	parameter: 69 body: 44
37	ExprTuple	45, 64
38	Lambda	parameter: 69 body: 46
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	Variable
46	Operation	operator: 58 operands: 59
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