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, Conditional, K, Lambda, U, V
from proveit.linear_algebra import VecSpaces
from proveit.logic import And, InClass, InSet

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = Lambda([U, V], Conditional(And(InSet(A, U), InSet(B, V)), And(InClass(U, sub_expr1), InClass(V, 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(U, V\right) \mapsto \left\{\left(A \in U\right) \land \left(B \in V\right) \textrm{ if } U \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right) ,  V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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