Theorem _psi_t_formula of type Forall

from the theory of proveit.physics.quantum.QPE

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.QPE import _psi_t_formula

# check that the built expression is the same as the stored expression
assert _psi_t_formula.expr == stored_expr
assert _psi_t_formula.expr._style_id == stored_expr._style_id
print("Passed sanity check: _psi_t_formula matches stored_expr")

Passed sanity check: _psi_t_formula matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{t \in \mathbb{N}^+}~\left(\lvert \psi_{t} \rangle = \left(\frac{1}{2^{\frac{t}{2}}} \cdot \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 62 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 33 operands: 9
7	Literal
8	ExprTuple	10, 11
9	ExprTuple	62, 12
10	Operation	operator: 13 operand: 62
11	Operation	operator: 31 operands: 15
12	Literal
13	Literal
14	ExprTuple	62
15	ExprTuple	16, 17
16	Operation	operator: 29 operands: 18
17	Operation	operator: 19 operand: 22
18	ExprTuple	63, 21
19	Literal
20	ExprTuple	22
21	Operation	operator: 57 operands: 23
22	Lambda	parameter: 54 body: 25
23	ExprTuple	61, 26
24	ExprTuple	54
25	Conditional	value: 27 condition: 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	62, 61
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	54, 37
35	Operation	operator: 57 operands: 38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operands: 42
38	ExprTuple	43, 44
39	Literal
40	ExprTuple	54, 62
41	Literal
42	ExprTuple	45, 46
43	Literal
44	Operation	operator: 47 operands: 48
45	Literal
46	Operation	operator: 49 operands: 50
47	Literal
48	ExprTuple	61, 51, 52, 53, 54
49	Literal
50	ExprTuple	55, 56
51	Literal
52	Literal
53	Literal
54	Variable
55	Operation	operator: 57 operands: 58
56	Operation	operator: 59 operand: 63
57	Literal
58	ExprTuple	61, 62
59	Literal
60	ExprTuple	63
61	Literal
62	Variable
63	Literal