Expression of type ExprTuple

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, Conditional, ExprTuple, K, Lambda, U, V, W
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, Exists, Forall, InClass, InSet

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = ExprTuple(Lambda(W, Conditional(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 = sub_expr1), condition = InSet(TensorProd(A, B), W)), InClass(W, sub_expr1))))

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())

\left(W \mapsto \left\{\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] \textrm{ if } W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 18 body: 3
2	ExprTuple	18
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 36 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	18, 42
9	Lambda	parameters: 22 body: 10
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 16
12	Operation	operator: 33 operands: 15
13	Literal
14	ExprTuple	16
15	ExprTuple	17, 18
16	Lambda	parameters: 19 body: 20
17	Operation	operator: 21 operands: 22
18	Variable
19	ExprTuple	40, 41
20	Conditional	value: 23 condition: 24
21	Literal
22	ExprTuple	38, 39
23	Operation	operator: 26 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 36 operands: 35
31	Operation	operator: 36 operands: 37
32	ExprTuple	38, 40
33	Literal
34	ExprTuple	39, 41
35	ExprTuple	40, 42
36	Literal
37	ExprTuple	41, 42
38	Variable
39	Variable
40	Variable
41	Variable
42	Operation	operator: 43 operand: 45
43	Literal
44	ExprTuple	45
45	Variable