Axiom _psi_t_def 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_axiom_expr # Load the stored axiom expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.QPE import _psi_t_def

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

Passed sanity check: _psi_t_def 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(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes}  \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes}  \ldots {\otimes}  \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\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: 31 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	31, 13
11	Operation	operator: 14 operand: 31
12	Operation	operator: 15 operands: 16
13	Literal
14	Literal
15	Literal
16	ExprTuple	17
17	ExprRange	lambda_map: 18 start_index: 19 end_index: 40
18	Lambda	parameter: 63 body: 20
19	Operation	operator: 21 operands: 22
20	Operation	operator: 37 operands: 23
21	Literal
22	ExprTuple	24, 50
23	ExprTuple	25, 26
24	Operation	operator: 61 operand: 31
25	Operation	operator: 43 operands: 28
26	Operation	operator: 29 operands: 30
27	ExprTuple	31
28	ExprTuple	50, 32
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Operation	operator: 57 operands: 35
33	Operation	operator: 46 operand: 40
34	Operation	operator: 37 operands: 38
35	ExprTuple	59, 39
36	ExprTuple	40
37	Literal
38	ExprTuple	41, 42
39	Operation	operator: 43 operands: 44
40	Literal
41	Operation	operator: 57 operands: 45
42	Operation	operator: 46 operand: 50
43	Literal
44	ExprTuple	50, 59
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50
48	Literal
49	Operation	operator: 51 operands: 52
50	Literal
51	Literal
52	ExprTuple	59, 53, 54, 55, 56
53	Literal
54	Literal
55	Operation	operator: 57 operands: 58
56	Literal
57	Literal
58	ExprTuple	59, 60
59	Literal
60	Operation	operator: 61 operand: 63
61	Literal
62	ExprTuple	63
63	Variable