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
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(alpha, Conditional(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)), InSet(alpha, RealNonNeg))))

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(\alpha \mapsto \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) \textrm{ if } \alpha \in \mathbb{R}^{\ge 0}\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: 28 body: 3
2	ExprTuple	28
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	28, 10
9	Lambda	parameter: 38 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 23 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 28
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 33 operand: 25
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	25
21	Literal
22	ExprTuple	38, 26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Operation	operator: 33 operand: 38
28	Variable
29	Literal
30	ExprTuple	35, 38
31	Literal
32	ExprTuple	36, 37
33	Literal
34	ExprTuple	38
35	Variable
36	Literal
37	Variable
38	Variable