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 ExprTuple, U, i, j, n
from proveit.core_expr_types import v_i, v_j
from proveit.linear_algebra import Adj, Unitary
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Interval, KroneckerDelta, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
expr = ExprTuple(Forall(instance_param_or_params = [i, j], instance_expr = Equals(Qmult(Bra(v_i), Adj(U), U, Ket(v_j)), KroneckerDelta(i, j)), domain = Interval(one, n)), InSet(U, Unitary(n)))

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_{i, j \in \{1~\ldotp \ldotp~n\}}~\left(\left(\langle v_{i} \rvert \thinspace U^{\dagger} \thinspace U \thinspace \lvert v_{j} \rangle\right) = \delta_{i, j}\right), U \in \textrm{U}\left(n\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
1	Operation	operator: 3 operand: 6
2	Operation	operator: 26 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	41, 7
6	Lambda	parameters: 24 body: 8
7	Operation	operator: 9 operand: 44
8	Conditional	value: 11 condition: 12
9	Literal
10	ExprTuple	44
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	Literal
22	ExprTuple	28, 29, 41, 30
23	Literal
24	ExprTuple	48, 49
25	ExprTuple	48, 31
26	Literal
27	ExprTuple	49, 31
28	Operation	operator: 32 operand: 40
29	Operation	operator: 34 operand: 41
30	Operation	operator: 36 operand: 42
31	Operation	operator: 38 operands: 39
32	Literal
33	ExprTuple	40
34	Literal
35	ExprTuple	41
36	Literal
37	ExprTuple	42
38	Literal
39	ExprTuple	43, 44
40	IndexedVar	variable: 46 index: 48
41	Variable
42	IndexedVar	variable: 46 index: 49
43	Literal
44	Variable
45	ExprTuple	48
46	Variable
47	ExprTuple	49
48	Variable
49	Variable