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(Mult(one, Exp(Mult(sqrt(two), Exp(two, sub_expr2)), Neg(one))), Mult(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(1 \cdot \left(\sqrt{2} \cdot 2^{\frac{1}{2} \cdot t}\right)^{-1}\right) = \left(1 \cdot \left(2^{-\frac{1}{2}} \cdot 2^{-\left(\frac{1}{2} \cdot t\right)}\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: 30 operands: 5
4	Operation	operator: 30 operands: 6
5	ExprTuple	36, 7
6	ExprTuple	36, 8
7	Operation	operator: 24 operands: 9
8	Operation	operator: 30 operands: 10
9	ExprTuple	11, 12
10	ExprTuple	13, 14
11	Operation	operator: 30 operands: 15
12	Operation	operator: 27 operand: 36
13	Operation	operator: 24 operands: 17
14	Operation	operator: 24 operands: 18
15	ExprTuple	19, 20
16	ExprTuple	36
17	ExprTuple	37, 21
18	ExprTuple	37, 22
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 27 operand: 32
22	Operation	operator: 27 operand: 29
23	ExprTuple	37, 32
24	Literal
25	ExprTuple	37, 29
26	ExprTuple	32
27	Literal
28	ExprTuple	29
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Operation	operator: 34 operands: 35
33	Variable
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Literal