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 Conditional, ConditionalSet
from proveit.logic import Equals, FALSE
from proveit.numbers import greater, greater_eq, one, subtract
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = subtract(_two_pow__t_minus_one, one)
expr = Equals(ConditionalSet(Conditional(_two_pow__t_minus_one, greater_eq(_two_pow__t_minus_one, sub_expr1)), Conditional(sub_expr1, greater(sub_expr1, _two_pow__t_minus_one))), ConditionalSet(_two_pow__t_minus_one, Conditional(sub_expr1, FALSE))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left\{\begin{array}{ccc}2^{t - 1} \textrm{ if } 2^{t - 1} \geq \left(2^{t - 1} - 1\right) \\ 2^{t - 1} - 1 \textrm{ if } \left(2^{t - 1} - 1\right) > 2^{t - 1}\end{array}\right.. =  \\ \left\{\begin{array}{ccc}2^{t - 1} \\ 2^{t - 1} - 1 \textrm{ if } \bot\end{array}\right.. \end{array} \end{array}

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.	()	(2)	('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, 9
6	Literal
7	ExprTuple	20, 10
8	Conditional	value: 20 condition: 11
9	Conditional	value: 18 condition: 12
10	Conditional	value: 18 condition: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Literal
14	Literal
15	ExprTuple	18, 20
16	Literal
17	ExprTuple	20, 18
18	Operation	operator: 25 operands: 19
19	ExprTuple	20, 28
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Literal
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Literal