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
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, Neg

# build up the expression from sub-expressions
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)

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_{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)

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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	28, 48, 29, 33, 30
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16, 17, 18
12	Operation	operator: 20 operands: 19
13	Operation	operator: 20 operands: 21
14	ExprRange	lambda_map: 22 start_index: 42 end_index: 38
15	Operation	operator: 46 operands: 23
16	ExprRange	lambda_map: 24 start_index: 42 end_index: 40
17	Operation	operator: 46 operands: 25
18	ExprRange	lambda_map: 26 start_index: 42 end_index: 43
19	ExprTuple	28, 27, 29, 33, 30
20	Literal
21	ExprTuple	28, 29, 30
22	Lambda	parameter: 57 body: 31
23	ExprTuple	48, 52
24	Lambda	parameter: 57 body: 32
25	ExprTuple	33, 52
26	Lambda	parameter: 57 body: 34
27	Operation	operator: 35 operand: 48
28	ExprRange	lambda_map: 37 start_index: 42 end_index: 38
29	ExprRange	lambda_map: 39 start_index: 42 end_index: 40
30	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
31	Operation	operator: 46 operands: 44
32	Operation	operator: 46 operands: 45
33	Variable
34	Operation	operator: 46 operands: 47
35	Literal
36	ExprTuple	48
37	Lambda	parameter: 57 body: 49
38	Variable
39	Lambda	parameter: 57 body: 50
40	Variable
41	Lambda	parameter: 57 body: 51
42	Literal
43	Variable
44	ExprTuple	49, 52
45	ExprTuple	50, 52
46	Literal
47	ExprTuple	51, 52
48	Variable
49	IndexedVar	variable: 53 index: 57
50	IndexedVar	variable: 54 index: 57
51	IndexedVar	variable: 55 index: 57
52	Literal
53	Variable
54	Variable
55	Variable
56	ExprTuple	57
57	Variable