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 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([Hspace, X], Forall(instance_param_or_params = [var_ket_psi], instance_expr = Forall(instance_param_or_params = [varphi], instance_expr = InClass(Qmult(var_ket_psi, bra_varphi), QmultCodomain), condition = InSet(ket_varphi, X)), domain = 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(\mathcal{H}, X\right) \mapsto \left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\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)\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	13, 24
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 28 body: 6
5	ExprTuple	28
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 19 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	28, 13
12	Lambda	parameter: 32 body: 14
13	Variable
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Operation	operator: 27 operand: 32
24	Variable
25	Literal
26	ExprTuple	28, 29
27	Literal
28	Variable
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Variable