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 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(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())

\left(\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..\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: 25 body: 3
2	ExprTuple	25
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 16 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	25, 10
9	Lambda	parameter: 29 body: 11
10	Variable
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Operation	operator: 24 operand: 29
21	Variable
22	Literal
23	ExprTuple	25, 26
24	Literal
25	Variable
26	Operation	operator: 27 operand: 29
27	Literal
28	ExprTuple	29
29	Variable