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 Add, Exp, Mult, Neg, frac, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
sub_expr2 = frac(t, two)
expr = Equals(Mult(Exp(two, Neg(sub_expr1)), Exp(two, Neg(Mult(sub_expr1, t)))), Mult(frac(one, Exp(two, subtract(frac(Add(t, one), two), sub_expr2))), frac(one, Exp(two, 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(2^{-\frac{1}{2}} \cdot 2^{-\left(\frac{1}{2} \cdot t\right)}\right) = \left(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \frac{1}{2^{\frac{t}{2}}}\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: 26 operands: 5
4	Operation	operator: 26 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	Operation	operator: 22 operands: 11
8	Operation	operator: 22 operands: 12
9	Operation	operator: 40 operands: 13
10	Operation	operator: 40 operands: 14
11	ExprTuple	44, 15
12	ExprTuple	44, 16
13	ExprTuple	42, 17
14	ExprTuple	42, 18
15	Operation	operator: 34 operand: 29
16	Operation	operator: 34 operand: 24
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	29
20	ExprTuple	24
21	ExprTuple	44, 25
22	Literal
23	ExprTuple	44, 37
24	Operation	operator: 26 operands: 27
25	Operation	operator: 38 operands: 28
26	Literal
27	ExprTuple	29, 43
28	ExprTuple	30, 31
29	Operation	operator: 40 operands: 32
30	Operation	operator: 40 operands: 33
31	Operation	operator: 34 operand: 37
32	ExprTuple	42, 44
33	ExprTuple	36, 44
34	Literal
35	ExprTuple	37
36	Operation	operator: 38 operands: 39
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	43, 42
40	Literal
41	ExprTuple	43, 44
42	Literal
43	Variable
44	Literal