Expression of type Forall

from the theory of proveit.linear_algebra.scalar_multiplication

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 x_1_to_n
from proveit.linear_algebra import lin_comb_axn
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(lin_comb_axn, V), 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_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) \in V\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	6
5	Conditional	value: 7 condition: 8
6	ExprRange	lambda_map: 9 start_index: 21 end_index: 22
7	Operation	operator: 23 operands: 10
8	Operation	operator: 11 operands: 12
9	Lambda	parameter: 34 body: 30
10	ExprTuple	13, 26
11	Literal
12	ExprTuple	14
13	Operation	operator: 15 operands: 16
14	ExprRange	lambda_map: 17 start_index: 21 end_index: 22
15	Literal
16	ExprTuple	18
17	Lambda	parameter: 34 body: 19
18	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
19	Operation	operator: 23 operands: 24
20	Lambda	parameter: 34 body: 25
21	Literal
22	Variable
23	Literal
24	ExprTuple	30, 26
25	Operation	operator: 27 operands: 28
26	Variable
27	Literal
28	ExprTuple	29, 30
29	IndexedVar	variable: 31 index: 34
30	IndexedVar	variable: 32 index: 34
31	Variable
32	Variable
33	ExprTuple	34
34	Variable