Expression of type ExprTuple

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 ExprTuple, 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 = ExprTuple(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(\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]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	14, 25
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 29 body: 7
6	ExprTuple	29
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 20 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	29, 14
13	Lambda	parameter: 33 body: 15
14	Variable
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Operation	operator: 28 operand: 33
25	Variable
26	Literal
27	ExprTuple	29, 30
28	Literal
29	Variable
30	Operation	operator: 31 operand: 33
31	Literal
32	ExprTuple	33
33	Variable