Theorem _alpha_ideal_case of type Implies

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 _alpha_ideal_case

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

Passed sanity check: _alpha_ideal_case matches stored_expr

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

\left(\left(2^{t} \cdot \varphi\right) \in \{0~\ldotp \ldotp~2^{t} - 1\}\right) \Rightarrow \left(\alpha_{2^{t} \cdot \varphi} = 1\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: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	17, 9
7	Literal
8	ExprTuple	10, 29
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operand: 17
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17
15	Literal
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	23, 22
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 25 operand: 29
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	30, 31
29	Literal
30	Literal
31	Literal