Expression of type Lambda

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, 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 47 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 20 body: 5
4	ExprTuple	20
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 38 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	20, 44
11	Lambda	parameters: 24 body: 12
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 18
14	Operation	operator: 35 operands: 17
15	Literal
16	ExprTuple	18
17	ExprTuple	19, 20
18	Lambda	parameters: 21 body: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	ExprTuple	42, 43
22	Conditional	value: 25 condition: 26
23	Literal
24	ExprTuple	40, 41
25	Operation	operator: 28 operands: 27
26	Operation	operator: 28 operands: 29
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 35 operands: 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 38 operands: 37
33	Operation	operator: 38 operands: 39
34	ExprTuple	40, 42
35	Literal
36	ExprTuple	41, 43
37	ExprTuple	42, 44
38	Literal
39	ExprTuple	43, 44
40	Variable
41	Variable
42	Variable
43	Variable
44	Operation	operator: 45 operand: 47
45	Literal
46	ExprTuple	47
47	Variable