Expression of type ExprTuple

from the theory of proveit.physics.quantum.algebra

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, Function, IndexedVar, Q, Variable, c, f, j, m, n
from proveit.linear_algebra import MatrixSpace, VecSum
from proveit.logic import Forall, InSet
from proveit.numbers import Complex, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = MatrixSpace(field = Complex, rows = n, columns = m)
sub_expr3 = [ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, j)]
sub_expr4 = Function(f, sub_expr3)
sub_expr5 = Function(Q, sub_expr3)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr3, instance_expr = InSet(sub_expr4, sub_expr2), condition = sub_expr5), InSet(VecSum(index_or_indices = sub_expr3, summand = sub_expr4, condition = sub_expr5), sub_expr2))

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(\forall_{c_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~\left(f\left(c_{1}, c_{2}, \ldots, c_{j}\right) \in \mathbb{C}^{n \times m}\right), \left[\sum_{c_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~f\left(c_{1}, c_{2}, \ldots, c_{j}\right)\right] \in \mathbb{C}^{n \times m}\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
1	Operation	operator: 3 operand: 6
2	Operation	operator: 13 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 16
6	Lambda	parameters: 23 body: 8
7	Operation	operator: 9 operand: 12
8	Conditional	value: 11 condition: 18
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operands: 14
12	Lambda	parameters: 23 body: 15
13	Literal
14	ExprTuple	17, 16
15	Conditional	value: 17 condition: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 23
18	Operation	operator: 22 operands: 23
19	Literal
20	NamedExprs	field: 24 rows: 25 columns: 26
21	Variable
22	Variable
23	ExprTuple	27
24	Literal
25	Variable
26	Variable
27	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
28	Lambda	parameter: 34 body: 31
29	Literal
30	Variable
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable