Expression of type Forall

from the theory of proveit.linear_algebra.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 import V
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.linear_algebra import VecAdd
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k], instance_expr = Equals(VecAdd(a_1_to_i, b_1_to_j, c_1_to_k), VecAdd(a_1_to_i, VecAdd(b_1_to_j), c_1_to_k)).with_wrapping_at(2), domain = V)

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}, c_{1}, c_{2}, \ldots, c_{k} \in V}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}+ c_{1} +  c_{2} +  \ldots +  c_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right)+ c_{1} +  c_{2} +  \ldots +  c_{k}\right) \end{array} \end{array}\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: 16 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, 15
11	Operation	operator: 29 operands: 16
12	Operation	operator: 29 operands: 17
13	ExprRange	lambda_map: 18 start_index: 42 end_index: 28
14	ExprRange	lambda_map: 19 start_index: 42 end_index: 43
15	ExprRange	lambda_map: 20 start_index: 42 end_index: 32
16	ExprTuple	21, 37, 23
17	ExprTuple	21, 22, 23
18	Lambda	parameter: 49 body: 24
19	Lambda	parameter: 49 body: 25
20	Lambda	parameter: 49 body: 26
21	ExprRange	lambda_map: 27 start_index: 42 end_index: 28
22	Operation	operator: 29 operands: 30
23	ExprRange	lambda_map: 31 start_index: 42 end_index: 32
24	Operation	operator: 35 operands: 33
25	Operation	operator: 35 operands: 34
26	Operation	operator: 35 operands: 36
27	Lambda	parameter: 49 body: 38
28	Variable
29	Literal
30	ExprTuple	37
31	Lambda	parameter: 49 body: 39
32	Variable
33	ExprTuple	38, 40
34	ExprTuple	46, 40
35	Literal
36	ExprTuple	39, 40
37	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
38	IndexedVar	variable: 44 index: 49
39	IndexedVar	variable: 45 index: 49
40	Variable
41	Lambda	parameter: 49 body: 46
42	Literal
43	Variable
44	Variable
45	Variable
46	IndexedVar	variable: 47 index: 49
47	Variable
48	ExprTuple	49
49	Variable