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, LinMap
from proveit.logic import Forall, InClass, 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(Hspace, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = InSet(Qmult(bra_varphi), LinMap(Hspace, Complex)), condition = InSet(ket_varphi, 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_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\left[\langle \varphi \rvert\right] \in \mathcal{L}\left(\mathcal{H}, \mathbb{C}\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: 26 body: 2
1	ExprTuple	26
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	26, 10
9	Lambda	parameter: 30 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 26
17	Operation	operator: 20 operand: 25
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operand: 30
20	Literal
21	ExprTuple	25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	Operation	operator: 28 operand: 30
26	Variable
27	Literal
28	Literal
29	ExprTuple	30
30	Variable