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, U, V, Variable, W, a, b, c, i, j, k
from proveit.logic import InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), IndexedVar(U, sub_expr1)), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), IndexedVar(V, sub_expr1)), one, j), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), IndexedVar(W, sub_expr1)), 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(a_{1} \in U_{1}\right), \left(a_{2} \in U_{2}\right), \ldots, \left(a_{i} \in U_{i}\right),\left(b_{1} \in V_{1}\right), \left(b_{2} \in V_{2}\right), \ldots, \left(b_{j} \in V_{j}\right),\left(c_{1} \in W_{1}\right), \left(c_{2} \in W_{2}\right), \ldots, \left(c_{k} \in W_{k}\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: 9 end_index: 5
2	ExprRange	lambda_map: 6 start_index: 9 end_index: 7
3	ExprRange	lambda_map: 8 start_index: 9 end_index: 10
4	Lambda	parameter: 31 body: 11
5	Variable
6	Lambda	parameter: 31 body: 12
7	Variable
8	Lambda	parameter: 31 body: 13
9	Literal
10	Variable
11	Operation	operator: 16 operands: 14
12	Operation	operator: 16 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	18, 19
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	22, 23
18	IndexedVar	variable: 24 index: 31
19	IndexedVar	variable: 25 index: 31
20	IndexedVar	variable: 26 index: 31
21	IndexedVar	variable: 27 index: 31
22	IndexedVar	variable: 28 index: 31
23	IndexedVar	variable: 29 index: 31
24	Variable
25	Variable
26	Variable
27	Variable
28	Variable
29	Variable
30	ExprTuple	31
31	Variable