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, InnerProd
from proveit.logic import Equals, Forall, InClass, InSet
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, var_ket_psi, varphi

# build up the expression from sub-expressions
expr = Lambda(Hspace, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = Equals(Qmult(bra_varphi), Lambda(var_ket_psi, Conditional(InnerProd(var_ket_psi, ket_varphi), InSet(var_ket_psi, Hspace)))), 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] = \left[\lvert \psi \rangle \mapsto \left\{\left \langle \lvert \psi \rangle, \lvert \varphi \rangle\right \rangle \textrm{ if } \lvert \psi \rangle \in \mathcal{H}\right..\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: 33 body: 2
1	ExprTuple	33
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	33, 10
9	Lambda	parameter: 36 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 29 operands: 16
14	Literal
15	ExprTuple	17, 18
16	ExprTuple	31, 33
17	Operation	operator: 19 operand: 23
18	Lambda	parameter: 32 body: 22
19	Literal
20	ExprTuple	23
21	ExprTuple	32
22	Conditional	value: 24 condition: 25
23	Operation	operator: 26 operand: 36
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Literal
27	Literal
28	ExprTuple	32, 31
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operand: 36
32	Variable
33	Variable
34	Literal
35	ExprTuple	36
36	Variable