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, ExprTuple, K, Lambda, 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
sub_expr1 = VecSpaces(K)
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [W], instance_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 = sub_expr1), condition = InSet(TensorProd(A, B), W)), domain = 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(K \mapsto \left[\forall_{W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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]\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: 48 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 21 body: 6
5	ExprTuple	21
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 39 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	21, 45
12	Lambda	parameters: 25 body: 13
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 36 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20, 21
19	Lambda	parameters: 22 body: 23
20	Operation	operator: 24 operands: 25
21	Variable
22	ExprTuple	43, 44
23	Conditional	value: 26 condition: 27
24	Literal
25	ExprTuple	41, 42
26	Operation	operator: 29 operands: 28
27	Operation	operator: 29 operands: 30
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 36 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 39 operands: 38
34	Operation	operator: 39 operands: 40
35	ExprTuple	41, 43
36	Literal
37	ExprTuple	42, 44
38	ExprTuple	43, 45
39	Literal
40	ExprTuple	44, 45
41	Variable
42	Variable
43	Variable
44	Variable
45	Operation	operator: 46 operand: 48
46	Literal
47	ExprTuple	48
48	Variable