Expression of type Equals

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, Lambda
from proveit.linear_algebra import Hspace, InnerProd
from proveit.logic import Equals, InSet
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, var_ket_psi

# build up the expression from sub-expressions
expr = Equals(Qmult(bra_varphi), Lambda(var_ket_psi, Conditional(InnerProd(var_ket_psi, ket_varphi), 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[\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]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 9
4	Lambda	parameter: 18 body: 8
5	Literal
6	ExprTuple	9
7	ExprTuple	18
8	Conditional	value: 10 condition: 11
9	Operation	operator: 12 operand: 22
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	Literal
14	ExprTuple	18, 17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 20 operand: 22
18	Variable
19	Variable
20	Literal
21	ExprTuple	22
22	Variable