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 import Function, V, s
from proveit.core_expr_types import Q__b_1_to_j, a_1_to_i, b_1_to_j, c_1_to_k, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(TensorProd(a_1_to_i, ScalarMult(Function(s, sub_expr1), f__b_1_to_j), c_1_to_k), V), condition = Q__b_1_to_j)

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_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\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: 30 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 30
7	Literal
8	ExprTuple	10, 11
9	Variable
10	Operation	operator: 12 operands: 13
11	Variable
12	Literal
13	ExprTuple	14, 15, 16
14	ExprRange	lambda_map: 17 start_index: 34 end_index: 18
15	Operation	operator: 19 operands: 20
16	ExprRange	lambda_map: 21 start_index: 34 end_index: 22
17	Lambda	parameter: 39 body: 23
18	Variable
19	Literal
20	ExprTuple	24, 25
21	Lambda	parameter: 39 body: 26
22	Variable
23	IndexedVar	variable: 27 index: 39
24	Operation	operator: 28 operands: 30
25	Operation	operator: 29 operands: 30
26	IndexedVar	variable: 31 index: 39
27	Variable
28	Variable
29	Variable
30	ExprTuple	32
31	Variable
32	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
33	Lambda	parameter: 39 body: 36
34	Literal
35	Variable
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable