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 Conditional, ExprTuple, Lambda, X
from proveit.linear_algebra import HilbertSpaces, Hspace, ScalarMult
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, var_ket_psi, var_ket_v, varphi

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = Forall(instance_param_or_params = [varphi], instance_expr = Equals(Qmult(var_ket_psi, bra_varphi), Lambda(var_ket_v, Conditional(ScalarMult(Qmult(bra_varphi, var_ket_v), var_ket_psi), InSet(var_ket_v, Hspace)))), condition = InSet(ket_varphi, Hspace)), domain = X), And(InClass(Hspace, HilbertSpaces), InClass(X, 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(\left(\mathcal{H}, X\right) \mapsto \left\{\forall_{\lvert \psi \rangle \in X}~\left[\forall_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\left(\lvert \psi \rangle \thinspace \langle \varphi \rvert\right) = \left[\lvert v \rangle \mapsto \left\{\left(\langle \varphi \rvert \thinspace \lvert v \rangle\right) \cdot \lvert \psi \rangle \textrm{ if } \lvert v \rangle \in \mathcal{H}\right..\right]\right)\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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	46, 24
3	Conditional	value: 4 condition: 5
4	Operation	operator: 20 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 45 body: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	45
13	Conditional	value: 17 condition: 18
14	ExprTuple	46, 19
15	Literal
16	ExprTuple	24, 19
17	Operation	operator: 20 operand: 23
18	Operation	operator: 42 operands: 22
19	Literal
20	Literal
21	ExprTuple	23
22	ExprTuple	45, 24
23	Lambda	parameter: 53 body: 25
24	Variable
25	Conditional	value: 26 condition: 27
26	Operation	operator: 28 operands: 29
27	Operation	operator: 42 operands: 30
28	Literal
29	ExprTuple	31, 32
30	ExprTuple	33, 46
31	Operation	operator: 47 operands: 34
32	Lambda	parameter: 50 body: 36
33	Operation	operator: 37 operand: 53
34	ExprTuple	45, 49
35	ExprTuple	50
36	Conditional	value: 38 condition: 39
37	Literal
38	Operation	operator: 40 operands: 41
39	Operation	operator: 42 operands: 43
40	Literal
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	50, 46
44	Operation	operator: 47 operands: 48
45	Variable
46	Variable
47	Literal
48	ExprTuple	49, 50
49	Operation	operator: 51 operand: 53
50	Variable
51	Literal
52	ExprTuple	53
53	Variable