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, 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)), 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}~|~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)\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	54, 56, 59
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 23 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 14 body: 15
11	Operation	operator: 62 operands: 16
12	Operation	operator: 62 operands: 17
13	Operation	operator: 62 operands: 18
14	ExprTuple	44, 50, 45, 64, 46
15	Conditional	value: 19 condition: 20
16	ExprTuple	54, 21
17	ExprTuple	56, 21
18	ExprTuple	59, 21
19	Operation	operator: 41 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28, 29, 30, 31, 32
25	Operation	operator: 34 operands: 33
26	Operation	operator: 34 operands: 35
27	ExprRange	lambda_map: 36 start_index: 58 end_index: 54
28	Operation	operator: 62 operands: 37
29	ExprRange	lambda_map: 38 start_index: 58 end_index: 56
30	Operation	operator: 62 operands: 39
31	ExprRange	lambda_map: 40 start_index: 58 end_index: 59
32	Operation	operator: 41 operands: 42
33	ExprTuple	44, 50, 45, 43, 46
34	Literal
35	ExprTuple	44, 45, 46
36	Lambda	parameter: 73 body: 47
37	ExprTuple	50, 68
38	Lambda	parameter: 73 body: 48
39	ExprTuple	64, 68
40	Lambda	parameter: 73 body: 49
41	Literal
42	ExprTuple	50, 64
43	Operation	operator: 51 operand: 64
44	ExprRange	lambda_map: 53 start_index: 58 end_index: 54
45	ExprRange	lambda_map: 55 start_index: 58 end_index: 56
46	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
47	Operation	operator: 62 operands: 60
48	Operation	operator: 62 operands: 61
49	Operation	operator: 62 operands: 63
50	Variable
51	Literal
52	ExprTuple	64
53	Lambda	parameter: 73 body: 65
54	Variable
55	Lambda	parameter: 73 body: 66
56	Variable
57	Lambda	parameter: 73 body: 67
58	Literal
59	Variable
60	ExprTuple	65, 68
61	ExprTuple	66, 68
62	Literal
63	ExprTuple	67, 68
64	Variable
65	IndexedVar	variable: 69 index: 73
66	IndexedVar	variable: 70 index: 73
67	IndexedVar	variable: 71 index: 73
68	Literal
69	Variable
70	Variable
71	Variable
72	ExprTuple	73
73	Variable