Expression of type Conditional

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 bra_varphi, ket_varphi, var_ket_psi, varphi

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [varphi], instance_expr = Equals(bra_varphi, Lambda(var_ket_psi, Conditional(InnerProd(ket_varphi, var_ket_psi), 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())

\left\{\forall_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\langle \varphi \rvert = \left[\lvert \psi \rangle \mapsto \left\{\left \langle \lvert \varphi \rangle, \lvert \psi \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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	28, 8
7	Lambda	parameter: 31 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 24 operands: 14
12	Literal
13	ExprTuple	15, 16
14	ExprTuple	26, 28
15	Operation	operator: 17 operand: 31
16	Lambda	parameter: 27 body: 19
17	Literal
18	ExprTuple	27
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	27, 28
26	Operation	operator: 29 operand: 31
27	Variable
28	Variable
29	Literal
30	ExprTuple	31
31	Variable