Expression of type Lambda

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, Lambda, U, n
from proveit.linear_algebra import Unitary
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
sub_expr1 = CartExp(Complex, n)
expr = Lambda(U, Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(U, var_ket_psi), sub_expr1), domain = sub_expr1), 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())

U \mapsto \left\{\forall_{\lvert \psi \rangle \in \mathbb{C}^{n}}~\left(\left(U \thinspace \lvert \psi \rangle\right) \in \mathbb{C}^{n}\right) \textrm{ if } U \in \textrm{U}\left(n\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 25 body: 2
1	ExprTuple	25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 17 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	25, 9
8	Lambda	parameter: 26 body: 11
9	Operation	operator: 12 operand: 28
10	ExprTuple	26
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	28
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	26, 20
19	Operation	operator: 21 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28
25	Variable
26	Variable
27	Literal
28	Variable