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 ExprRange, ExprTuple, IndexedVar, K, U, V, Variable, W, i, k
from proveit.linear_algebra import VecSpaces
from proveit.logic import InClass
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = VecSpaces(K)
expr = ExprTuple(ExprRange(sub_expr1, InClass(IndexedVar(U, sub_expr1), sub_expr2), one, i), InClass(V, sub_expr2), ExprRange(sub_expr1, InClass(IndexedVar(W, sub_expr1), sub_expr2), one, k))

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_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), \left(U_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), \ldots, \left(U_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right),\left(W_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), \left(W_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), \ldots, \left(W_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2, 3
1	ExprRange	lambda_map: 4 start_index: 8 end_index: 5
2	Operation	operator: 14 operands: 6
3	ExprRange	lambda_map: 7 start_index: 8 end_index: 9
4	Lambda	parameter: 24 body: 10
5	Variable
6	ExprTuple	11, 18
7	Lambda	parameter: 24 body: 12
8	Literal
9	Variable
10	Operation	operator: 14 operands: 13
11	Variable
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 18
14	Literal
15	ExprTuple	17, 18
16	IndexedVar	variable: 19 index: 24
17	IndexedVar	variable: 20 index: 24
18	Operation	operator: 22 operand: 25
19	Variable
20	Variable
21	ExprTuple	24
22	Literal
23	ExprTuple	25
24	Variable
25	Variable