Expression of type Conditional

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, K, 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 = 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\{\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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