Expression of type Forall

from the theory of proveit.numbers.addition

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.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Equals(Add(a_1_to_i, zero, b_1_to_j), Add(a_1_to_i, b_1_to_j)), 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_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + 0+ b_{1} +  b_{2} +  \ldots +  b_{j}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}\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: 17 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprRange	lambda_map: 18 start_index: 28 end_index: 26
14	ExprRange	lambda_map: 19 start_index: 28 end_index: 29
15	ExprTuple	21, 20, 22
16	Literal
17	ExprTuple	21, 22
18	Lambda	parameter: 39 body: 23
19	Lambda	parameter: 39 body: 24
20	Literal
21	ExprRange	lambda_map: 25 start_index: 28 end_index: 26
22	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
23	Operation	operator: 31 operands: 30
24	Operation	operator: 31 operands: 32
25	Lambda	parameter: 39 body: 33
26	Variable
27	Lambda	parameter: 39 body: 34
28	Literal
29	Variable
30	ExprTuple	33, 35
31	Literal
32	ExprTuple	34, 35
33	IndexedVar	variable: 36 index: 39
34	IndexedVar	variable: 37 index: 39
35	Literal
36	Variable
37	Variable
38	ExprTuple	39
39	Variable