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, c
from proveit.linear_algebra import HilbertSpaces, Hspace
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(c, Conditional(Forall(instance_param_or_params = [Hspace], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(c, var_ket_psi), Hspace), domain = Hspace), domain = HilbertSpaces), InSet(c, Complex))))

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(c \mapsto \left\{\forall_{\mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(c \thinspace \lvert \psi \rangle\right) \in \mathcal{H}\right)\right] \textrm{ if } c \in \mathbb{C}\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	parameter: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 25 operands: 7
6	ExprTuple	8
7	ExprTuple	31, 9
8	Lambda	parameter: 28 body: 11
9	Literal
10	ExprTuple	28
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 18
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	28, 19
18	Lambda	parameter: 32 body: 21
19	Literal
20	ExprTuple	32
21	Conditional	value: 22 condition: 23
22	Operation	operator: 25 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	32, 28
27	Operation	operator: 29 operands: 30
28	Variable
29	Literal
30	ExprTuple	31, 32
31	Variable
32	Variable