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
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 = ExprTuple(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(\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..\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: 2 body: 3
2	ExprTuple	21, 22
3	Conditional	value: 4 condition: 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	19, 21
14	Literal
15	ExprTuple	20, 22
16	ExprTuple	21, 23
17	Literal
18	ExprTuple	22, 23
19	Variable
20	Variable
21	Variable
22	Variable
23	Operation	operator: 24 operand: 26
24	Literal
25	ExprTuple	26
26	Variable