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, X
from proveit.linear_algebra import Hspace
from proveit.logic import Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain, bra_varphi, ket_varphi, var_ket_psi, varphi

# build up the expression from sub-expressions
expr = Lambda(var_ket_psi, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = InClass(Qmult(var_ket_psi, bra_varphi), QmultCodomain), condition = InSet(ket_varphi, X)), InSet(var_ket_psi, 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())

\lvert \psi \rangle \mapsto \left\{\forall_{\varphi~|~\lvert \varphi \rangle \in X}~\left(\left(\lvert \psi \rangle \thinspace \langle \varphi \rvert\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \textrm{ if } \lvert \psi \rangle \in \mathcal{H}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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