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, b, c_1_to_j, Neg(d), e_1_to_k), Add(a_1_to_i, c_1_to_j, e_1_to_k)), domain = Complex, condition = Equals(b, d)), 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}~|~b = d}~\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	52, 54, 57
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 21 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 12 body: 13
9	Operation	operator: 60 operands: 14
10	Operation	operator: 60 operands: 15
11	Operation	operator: 60 operands: 16
12	ExprTuple	42, 48, 43, 62, 44
13	Conditional	value: 17 condition: 18
14	ExprTuple	52, 19
15	ExprTuple	54, 19
16	ExprTuple	57, 19
17	Operation	operator: 39 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27, 28, 29, 30
23	Operation	operator: 32 operands: 31
24	Operation	operator: 32 operands: 33
25	ExprRange	lambda_map: 34 start_index: 56 end_index: 52
26	Operation	operator: 60 operands: 35
27	ExprRange	lambda_map: 36 start_index: 56 end_index: 54
28	Operation	operator: 60 operands: 37
29	ExprRange	lambda_map: 38 start_index: 56 end_index: 57
30	Operation	operator: 39 operands: 40
31	ExprTuple	42, 48, 43, 41, 44
32	Literal
33	ExprTuple	42, 43, 44
34	Lambda	parameter: 71 body: 45
35	ExprTuple	48, 66
36	Lambda	parameter: 71 body: 46
37	ExprTuple	62, 66
38	Lambda	parameter: 71 body: 47
39	Literal
40	ExprTuple	48, 62
41	Operation	operator: 49 operand: 62
42	ExprRange	lambda_map: 51 start_index: 56 end_index: 52
43	ExprRange	lambda_map: 53 start_index: 56 end_index: 54
44	ExprRange	lambda_map: 55 start_index: 56 end_index: 57
45	Operation	operator: 60 operands: 58
46	Operation	operator: 60 operands: 59
47	Operation	operator: 60 operands: 61
48	Variable
49	Literal
50	ExprTuple	62
51	Lambda	parameter: 71 body: 63
52	Variable
53	Lambda	parameter: 71 body: 64
54	Variable
55	Lambda	parameter: 71 body: 65
56	Literal
57	Variable
58	ExprTuple	63, 66
59	ExprTuple	64, 66
60	Literal
61	ExprTuple	65, 66
62	Variable
63	IndexedVar	variable: 67 index: 71
64	IndexedVar	variable: 68 index: 71
65	IndexedVar	variable: 69 index: 71
66	Literal
67	Variable
68	Variable
69	Variable
70	ExprTuple	71
71	Variable