Expression of type Forall

from the theory of proveit.linear_algebra.tensors

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 V_1_to_i, a_1_to_i
from proveit.linear_algebra import TensorProd
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(TensorProd(a_1_to_i), TensorProd(V_1_to_i)), domains = [V_1_to_i])

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_{\left(a_{1} \in V_{1}\right), \left(a_{2} \in V_{2}\right), \ldots, \left(a_{i} \in V_{i}\right)}~\left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}\right) \in \left(V_{1} {\otimes}  V_{2} {\otimes}  \ldots {\otimes}  V_{i}\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: 13 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 24 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	ExprRange	lambda_map: 16 start_index: 22 end_index: 23
13	ExprTuple	17
14	Literal
15	ExprTuple	18
16	Lambda	parameter: 31 body: 19
17	ExprRange	lambda_map: 20 start_index: 22 end_index: 23
18	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
19	Operation	operator: 24 operands: 25
20	Lambda	parameter: 31 body: 26
21	Lambda	parameter: 31 body: 27
22	Literal
23	Variable
24	Literal
25	ExprTuple	26, 27
26	IndexedVar	variable: 28 index: 31
27	IndexedVar	variable: 29 index: 31
28	Variable
29	Variable
30	ExprTuple	31
31	Variable