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, InSet

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

\left(\left(A, B\right) \mapsto \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) \textrm{ if } \left(A {\otimes} B\right) \in W\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	parameters: 14 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 25 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 13 operands: 14
10	Variable
11	ExprTuple	32, 33
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	30, 31
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	ExprTuple	30, 32
25	Literal
26	ExprTuple	31, 33
27	ExprTuple	32, 34
28	Literal
29	ExprTuple	33, 34
30	Variable
31	Variable
32	Variable
33	Variable
34	Operation	operator: 35 operand: 37
35	Literal
36	ExprTuple	37
37	Variable