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
from proveit.linear_algebra import HilbertSpaces, Hspace, TensorProd
from proveit.logic import Equals, Forall, InClass
from proveit.physics.quantum import Qmult, var_ket_psi, var_ket_varphi

# build up the expression from sub-expressions
expr = Lambda(Hspace, Conditional(Forall(instance_param_or_params = [var_ket_psi, var_ket_varphi], instance_expr = Equals(Qmult(var_ket_psi, var_ket_varphi), TensorProd(var_ket_psi, var_ket_varphi)), domain = Hspace), InClass(Hspace, HilbertSpaces)))

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())

\mathcal{H} \mapsto \left\{\forall_{\lvert \psi \rangle, \lvert \varphi \rangle \in \mathcal{H}}~\left(\left(\lvert \psi \rangle \thinspace \lvert \varphi \rangle\right) = \left(\lvert \psi \rangle {\otimes} \lvert \varphi \rangle\right)\right) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 30 body: 2
1	ExprTuple	30
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	30, 10
9	Lambda	parameters: 24 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 24
19	Operation	operator: 23 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Literal
24	ExprTuple	28, 29
25	ExprTuple	28, 30
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Variable
30	Variable