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, Variable, W, a, c, d, f, i, 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}")
sub_expr2 = IndexedVar(U, sub_expr1)
sub_expr3 = IndexedVar(W, sub_expr1)
expr = ExprTuple(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), sub_expr3), one, k), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InSet(IndexedVar(f, sub_expr1), sub_expr3), 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(c_{1} \in W_{1}\right), \left(c_{2} \in W_{2}\right), \ldots, \left(c_{k} \in W_{k}\right),\left(d_{1} \in U_{1}\right), \left(d_{2} \in U_{2}\right), \ldots, \left(d_{i} \in U_{i}\right),\left(f_{1} \in W_{1}\right), \left(f_{2} \in W_{2}\right), \ldots, \left(f_{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, 4
1	ExprRange	lambda_map: 5 start_index: 10 end_index: 8
2	ExprRange	lambda_map: 6 start_index: 10 end_index: 11
3	ExprRange	lambda_map: 7 start_index: 10 end_index: 8
4	ExprRange	lambda_map: 9 start_index: 10 end_index: 11
5	Lambda	parameter: 34 body: 12
6	Lambda	parameter: 34 body: 13
7	Lambda	parameter: 34 body: 14
8	Variable
9	Lambda	parameter: 34 body: 15
10	Literal
11	Variable
12	Operation	operator: 19 operands: 16
13	Operation	operator: 19 operands: 17
14	Operation	operator: 19 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	21, 24
17	ExprTuple	22, 26
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25, 26
21	IndexedVar	variable: 27 index: 34
22	IndexedVar	variable: 28 index: 34
23	IndexedVar	variable: 29 index: 34
24	IndexedVar	variable: 30 index: 34
25	IndexedVar	variable: 31 index: 34
26	IndexedVar	variable: 32 index: 34
27	Variable
28	Variable
29	Variable
30	Variable
31	Variable
32	Variable
33	ExprTuple	34
34	Variable