Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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 t
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, frac, one, sqrt, two

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
sub_expr2 = Mult(sub_expr1, t)
expr = Equals(Exp(Mult(sqrt(two), Exp(two, sub_expr2)), Neg(one)), Mult(Exp(two, Neg(sub_expr1)), Exp(two, Neg(sub_expr2))))

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(\sqrt{2} \cdot 2^{\frac{1}{2} \cdot t}\right)^{-1} = \left(2^{-\frac{1}{2}} \cdot 2^{-\left(\frac{1}{2} \cdot t\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: 20 operands: 5
4	Operation	operator: 26 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	Operation	operator: 26 operands: 11
8	Operation	operator: 23 operand: 32
9	Operation	operator: 20 operands: 13
10	Operation	operator: 20 operands: 14
11	ExprTuple	15, 16
12	ExprTuple	32
13	ExprTuple	33, 17
14	ExprTuple	33, 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 23 operand: 28
18	Operation	operator: 23 operand: 25
19	ExprTuple	33, 28
20	Literal
21	ExprTuple	33, 25
22	ExprTuple	28
23	Literal
24	ExprTuple	25
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Operation	operator: 30 operands: 31
29	Variable
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Literal