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 A, B, K, U, V, W
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, Exists, Forall, InSet

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B], instance_expr = Exists(instance_param_or_params = [U, V], instance_expr = And(InSet(A, U), InSet(B, V)), domain = VecSpaces(K)), condition = InSet(TensorProd(A, B), W))

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, B~|~\left(A {\otimes} B\right) \in W}~\left[\exists_{U, V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(\left(A \in U\right) \land \left(B \in V\right)\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: 16 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 27 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 13 body: 14
11	Operation	operator: 15 operands: 16
12	Variable
13	ExprTuple	34, 35
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	32, 33
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 27 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	ExprTuple	32, 34
27	Literal
28	ExprTuple	33, 35
29	ExprTuple	34, 36
30	Literal
31	ExprTuple	35, 36
32	Variable
33	Variable
34	Variable
35	Variable
36	Operation	operator: 37 operand: 39
37	Literal
38	ExprTuple	39
39	Variable