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, c
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_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, d_1_to_k], instance_expr = Equals(VecAdd(a_1_to_i, b_1_to_j, c, d_1_to_k), VecAdd(a_1_to_i, c, b_1_to_j, d_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, d_{1}, d_{2}, \ldots, d_{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+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i} + c+ b_{1} +  b_{2} +  \ldots +  b_{j}+ d_{1} +  d_{2} +  \ldots +  d_{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: 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, 15, 16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprRange	lambda_map: 20 start_index: 36 end_index: 32
14	ExprRange	lambda_map: 21 start_index: 36 end_index: 34
15	Operation	operator: 40 operands: 22
16	ExprRange	lambda_map: 23 start_index: 36 end_index: 37
17	ExprTuple	24, 25, 29, 26
18	Literal
19	ExprTuple	24, 29, 25, 26
20	Lambda	parameter: 50 body: 27
21	Lambda	parameter: 50 body: 28
22	ExprTuple	29, 45
23	Lambda	parameter: 50 body: 30
24	ExprRange	lambda_map: 31 start_index: 36 end_index: 32
25	ExprRange	lambda_map: 33 start_index: 36 end_index: 34
26	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
27	Operation	operator: 40 operands: 38
28	Operation	operator: 40 operands: 39
29	Variable
30	Operation	operator: 40 operands: 41
31	Lambda	parameter: 50 body: 42
32	Variable
33	Lambda	parameter: 50 body: 43
34	Variable
35	Lambda	parameter: 50 body: 44
36	Literal
37	Variable
38	ExprTuple	42, 45
39	ExprTuple	43, 45
40	Literal
41	ExprTuple	44, 45
42	IndexedVar	variable: 46 index: 50
43	IndexedVar	variable: 47 index: 50
44	IndexedVar	variable: 48 index: 50
45	Variable
46	Variable
47	Variable
48	Variable
49	ExprTuple	50
50	Variable