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, LinMap
from proveit.logic import InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, varphi

# build up the expression from sub-expressions
expr = Lambda(varphi, Conditional(InSet(Qmult(bra_varphi), LinMap(Hspace, Complex)), InSet(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())

\varphi \mapsto \left\{\left[\langle \varphi \rvert\right] \in \mathcal{L}\left(\mathcal{H}, \mathbb{C}\right) \textrm{ if } \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	parameter: 20 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 16
7	Operation	operator: 10 operand: 15
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operand: 20
10	Literal
11	ExprTuple	15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	Operation	operator: 18 operand: 20
16	Variable
17	Literal
18	Literal
19	ExprTuple	20
20	Variable