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 A, alpha, beta, delta, gamma
from proveit.logic import Equals
from proveit.numbers import Mult
from proveit.physics.quantum import Qmult, bra_varphi, ket_psi

# build up the expression from sub-expressions
expr = Equals(Qmult(bra_varphi, alpha, A, beta, ket_psi, gamma, bra_varphi, delta), Qmult(Mult(alpha, beta, gamma, delta), bra_varphi, A, ket_psi, bra_varphi))

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 \thinspace \alpha \thinspace A \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right) = \left(\left(\alpha \cdot \beta \cdot \gamma \cdot \delta\right) \thinspace \langle \varphi \rvert \thinspace A \thinspace \lvert \psi \rangle \thinspace \langle \varphi \rvert\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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	11, 18, 9, 19, 10, 20, 11, 21
6	Literal
7	ExprTuple	8, 11, 9, 10, 11
8	Operation	operator: 12 operands: 13
9	Variable
10	Operation	operator: 14 operand: 22
11	Operation	operator: 16 operand: 23
12	Literal
13	ExprTuple	18, 19, 20, 21
14	Literal
15	ExprTuple	22
16	Literal
17	ExprTuple	23
18	Variable
19	Variable
20	Variable
21	Variable
22	Variable
23	Variable