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 Conditional, ExprTuple, Lambda, U, alpha, n
from proveit.linear_algebra import Norm, Unitary
from proveit.logic import CartExp, Equals, Forall, InSet
from proveit.numbers import Complex, RealNonNeg
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(U, Conditional(Forall(instance_param_or_params = [alpha], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = Equals(Norm(Qmult(U, var_ket_psi)), alpha), domain = CartExp(Complex, n), condition = Equals(Norm(var_ket_psi), alpha)), domain = RealNonNeg), 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(U \mapsto \left\{\forall_{\alpha \in \mathbb{R}^{\ge 0}}~\left[\forall_{\lvert \psi \rangle \in \mathbb{C}^{n}~|~\left \|\lvert \psi \rangle\right \| = \alpha}~\left(\left \|U \thinspace \lvert \psi \rangle\right \| = \alpha\right)\right] \textrm{ if } U \in \textrm{U}\left(n\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 45 body: 3
2	ExprTuple	45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 16 operand: 8
5	Operation	operator: 31 operands: 7
6	ExprTuple	8
7	ExprTuple	45, 9
8	Lambda	parameter: 38 body: 11
9	Operation	operator: 12 operand: 47
10	ExprTuple	38
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	47
14	Operation	operator: 16 operand: 19
15	Operation	operator: 31 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	38, 20
19	Lambda	parameter: 48 body: 21
20	Literal
21	Conditional	value: 22 condition: 23
22	Operation	operator: 33 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 38
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 43 operand: 35
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	ExprTuple	35
31	Literal
32	ExprTuple	48, 36
33	Literal
34	ExprTuple	37, 38
35	Operation	operator: 39 operands: 40
36	Operation	operator: 41 operands: 42
37	Operation	operator: 43 operand: 48
38	Variable
39	Literal
40	ExprTuple	45, 48
41	Literal
42	ExprTuple	46, 47
43	Literal
44	ExprTuple	48
45	Variable
46	Literal
47	Variable
48	Variable