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, InnerProd
from proveit.logic import Equals, InSet
from proveit.physics.quantum import bra_varphi, ket_varphi, var_ket_psi, varphi

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(varphi, Conditional(Equals(bra_varphi, Lambda(var_ket_psi, Conditional(InnerProd(ket_varphi, var_ket_psi), InSet(var_ket_psi, 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\{\langle \varphi \rvert = \left[\lvert \psi \rangle \mapsto \left\{\left \langle \lvert \varphi \rangle, \lvert \psi \rangle\right \rangle \textrm{ if } \lvert \psi \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: 24 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 17 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	19, 21
8	Operation	operator: 10 operand: 24
9	Lambda	parameter: 20 body: 12
10	Literal
11	ExprTuple	20
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 22 operand: 24
20	Variable
21	Variable
22	Literal
23	ExprTuple	24
24	Variable