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 Hspace, InnerProd
from proveit.logic import Equals, InSet
from proveit.physics.quantum import bra_varphi, ket_varphi, var_ket_psi

# build up the expression from sub-expressions
expr = Conditional(Equals(bra_varphi, Lambda(var_ket_psi, Conditional(InnerProd(ket_varphi, var_ket_psi), InSet(var_ket_psi, Hspace)))), 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())

\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] \textrm{ if } \lvert \varphi \rangle \in \mathcal{H}\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 operands: 4
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	17, 19
6	Operation	operator: 8 operand: 22
7	Lambda	parameter: 18 body: 10
8	Literal
9	ExprTuple	18
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 20 operand: 22
18	Variable
19	Variable
20	Literal
21	ExprTuple	22
22	Variable