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
from proveit.linear_algebra import HilbertSpaces, Hspace, InnerProd
from proveit.logic import Equals, Forall, InClass, InSet
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, var_ket_psi, varphi

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(Hspace, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = Equals(Qmult(bra_varphi), Lambda(var_ket_psi, Conditional(InnerProd(var_ket_psi, ket_varphi), InSet(var_ket_psi, Hspace)))), condition = InSet(ket_varphi, Hspace)), InClass(Hspace, 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(\mathcal{H} \mapsto \left\{\forall_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\left[\langle \varphi \rvert\right] = \left[\lvert \psi \rangle \mapsto \left\{\left \langle \lvert \psi \rangle, \lvert \varphi \rangle\right \rangle \textrm{ if } \lvert \psi \rangle \in \mathcal{H}\right..\right]\right) \textrm{ if } \mathcal{H} \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	parameter: 34 body: 3
2	ExprTuple	34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	34, 11
10	Lambda	parameter: 37 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 30 operands: 17
15	Literal
16	ExprTuple	18, 19
17	ExprTuple	32, 34
18	Operation	operator: 20 operand: 24
19	Lambda	parameter: 33 body: 23
20	Literal
21	ExprTuple	24
22	ExprTuple	33
23	Conditional	value: 25 condition: 26
24	Operation	operator: 27 operand: 37
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Literal
28	Literal
29	ExprTuple	33, 32
30	Literal
31	ExprTuple	33, 34
32	Operation	operator: 35 operand: 37
33	Variable
34	Variable
35	Literal
36	ExprTuple	37
37	Variable