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 Qmult, 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(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())

\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()

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	31, 8
7	Lambda	parameter: 34 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 27 operands: 14
12	Literal
13	ExprTuple	15, 16
14	ExprTuple	29, 31
15	Operation	operator: 17 operand: 21
16	Lambda	parameter: 30 body: 20
17	Literal
18	ExprTuple	21
19	ExprTuple	30
20	Conditional	value: 22 condition: 23
21	Operation	operator: 24 operand: 34
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	30, 29
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 32 operand: 34
30	Variable
31	Variable
32	Literal
33	ExprTuple	34
34	Variable