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.logic import Equals
from proveit.numbers import Exp, Mult, Neg, frac, one, two
from proveit.physics.quantum.QPE import _t

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

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