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, NaturalPos, RealNonNeg
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [U], instance_expr = 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), domain = Unitary(n)), InSet(n, NaturalPos))))

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(n \mapsto \left\{\forall_{U \in \textrm{U}\left(n\right)}~\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]\right] \textrm{ if } n \in \mathbb{N}^+\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: 54 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 23 operand: 7
4	Operation	operator: 38 operands: 6
5	ExprTuple	7
6	ExprTuple	54, 8
7	Lambda	parameter: 52 body: 10
8	Literal
9	ExprTuple	52
10	Conditional	value: 11 condition: 12
11	Operation	operator: 23 operand: 15
12	Operation	operator: 38 operands: 14
13	ExprTuple	15
14	ExprTuple	52, 16
15	Lambda	parameter: 45 body: 18
16	Operation	operator: 19 operand: 54
17	ExprTuple	45
18	Conditional	value: 21 condition: 22
19	Literal
20	ExprTuple	54
21	Operation	operator: 23 operand: 26
22	Operation	operator: 38 operands: 25
23	Literal
24	ExprTuple	26
25	ExprTuple	45, 27
26	Lambda	parameter: 55 body: 28
27	Literal
28	Conditional	value: 29 condition: 30
29	Operation	operator: 40 operands: 31
30	Operation	operator: 32 operands: 33
31	ExprTuple	34, 45
32	Literal
33	ExprTuple	35, 36
34	Operation	operator: 50 operand: 42
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	ExprTuple	42
38	Literal
39	ExprTuple	55, 43
40	Literal
41	ExprTuple	44, 45
42	Operation	operator: 46 operands: 47
43	Operation	operator: 48 operands: 49
44	Operation	operator: 50 operand: 55
45	Variable
46	Literal
47	ExprTuple	52, 55
48	Literal
49	ExprTuple	53, 54
50	Literal
51	ExprTuple	55
52	Variable
53	Literal
54	Variable
55	Variable