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 Hspace, ScalarMult
from proveit.logic import Equals, 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(varphi, Conditional(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)))), InSet(ket_varphi, 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(\varphi \mapsto \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] \textrm{ if } \lvert \varphi \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: 30 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 23
8	Operation	operator: 24 operands: 11
9	Lambda	parameter: 27 body: 13
10	Operation	operator: 14 operand: 30
11	ExprTuple	22, 26
12	ExprTuple	27
13	Conditional	value: 15 condition: 16
14	Literal
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	27, 23
21	Operation	operator: 24 operands: 25
22	Variable
23	Variable
24	Literal
25	ExprTuple	26, 27
26	Operation	operator: 28 operand: 30
27	Variable
28	Literal
29	ExprTuple	30
30	Variable