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, 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))

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}~|~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)

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	30, 36, 31, 50, 32
5	Conditional	value: 6 condition: 7
6	Operation	operator: 27 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15, 16, 17, 18
11	Operation	operator: 20 operands: 19
12	Operation	operator: 20 operands: 21
13	ExprRange	lambda_map: 22 start_index: 44 end_index: 40
14	Operation	operator: 48 operands: 23
15	ExprRange	lambda_map: 24 start_index: 44 end_index: 42
16	Operation	operator: 48 operands: 25
17	ExprRange	lambda_map: 26 start_index: 44 end_index: 45
18	Operation	operator: 27 operands: 28
19	ExprTuple	30, 36, 31, 29, 32
20	Literal
21	ExprTuple	30, 31, 32
22	Lambda	parameter: 59 body: 33
23	ExprTuple	36, 54
24	Lambda	parameter: 59 body: 34
25	ExprTuple	50, 54
26	Lambda	parameter: 59 body: 35
27	Literal
28	ExprTuple	36, 50
29	Operation	operator: 37 operand: 50
30	ExprRange	lambda_map: 39 start_index: 44 end_index: 40
31	ExprRange	lambda_map: 41 start_index: 44 end_index: 42
32	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
33	Operation	operator: 48 operands: 46
34	Operation	operator: 48 operands: 47
35	Operation	operator: 48 operands: 49
36	Variable
37	Literal
38	ExprTuple	50
39	Lambda	parameter: 59 body: 51
40	Variable
41	Lambda	parameter: 59 body: 52
42	Variable
43	Lambda	parameter: 59 body: 53
44	Literal
45	Variable
46	ExprTuple	51, 54
47	ExprTuple	52, 54
48	Literal
49	ExprTuple	53, 54
50	Variable
51	IndexedVar	variable: 55 index: 59
52	IndexedVar	variable: 56 index: 59
53	IndexedVar	variable: 57 index: 59
54	Literal
55	Variable
56	Variable
57	Variable
58	ExprTuple	59
59	Variable