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 Hspace, TensorProd
from proveit.logic import And, Equals, InSet
from proveit.physics.quantum import Qmult, var_ket_psi, var_ket_varphi

# build up the expression from sub-expressions
expr = Lambda([var_ket_psi, var_ket_varphi], Conditional(Equals(Qmult(var_ket_psi, var_ket_varphi), TensorProd(var_ket_psi, var_ket_varphi)), And(InSet(var_ket_psi, Hspace), InSet(var_ket_varphi, Hspace))))

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(\lvert \psi \rangle, \lvert \varphi \rangle\right) \mapsto \left\{\left(\lvert \psi \rangle \thinspace \lvert \varphi \rangle\right) = \left(\lvert \psi \rangle {\otimes} \lvert \varphi \rangle\right) \textrm{ if } \lvert \psi \rangle \in \mathcal{H} ,  \lvert \varphi \rangle \in \mathcal{H}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 14 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operands: 14
9	Operation	operator: 13 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Literal
13	Literal
14	ExprTuple	18, 19
15	ExprTuple	18, 20
16	Literal
17	ExprTuple	19, 20
18	Variable
19	Variable
20	Variable