Expression of type Forall

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 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 Equals, Forall
from proveit.numbers import Add, Complex, Natural, Neg

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [i, j, k], instance_expr = 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), domain = 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())

\forall_{i, j, k \in \mathbb{N}}~\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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	52, 54, 57
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 24 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 14 body: 15
11	Operation	operator: 60 operands: 16
12	Operation	operator: 60 operands: 17
13	Operation	operator: 60 operands: 18
14	ExprTuple	42, 62, 43, 47, 44
15	Conditional	value: 19 condition: 20
16	ExprTuple	52, 21
17	ExprTuple	54, 21
18	ExprTuple	57, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29, 30, 31, 32
26	Operation	operator: 34 operands: 33
27	Operation	operator: 34 operands: 35
28	ExprRange	lambda_map: 36 start_index: 56 end_index: 52
29	Operation	operator: 60 operands: 37
30	ExprRange	lambda_map: 38 start_index: 56 end_index: 54
31	Operation	operator: 60 operands: 39
32	ExprRange	lambda_map: 40 start_index: 56 end_index: 57
33	ExprTuple	42, 41, 43, 47, 44
34	Literal
35	ExprTuple	42, 43, 44
36	Lambda	parameter: 71 body: 45
37	ExprTuple	62, 66
38	Lambda	parameter: 71 body: 46
39	ExprTuple	47, 66
40	Lambda	parameter: 71 body: 48
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	Variable
48	Operation	operator: 60 operands: 61
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