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