Expression of type And

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.logic import And
from proveit.numbers import LessEq, one, subtract, two
from proveit.physics.quantum.QPE import _e_value, _two_pow__t_minus_one

# build up the expression from sub-expressions
expr = And(LessEq(one, _e_value), LessEq(_e_value, subtract(_two_pow__t_minus_one, two)))

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(1 \leq \left(2^{t - n} - 1\right)\right) \land \left(\left(2^{t - n} - 1\right) \leq \left(2^{t - 1} - 2\right)\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',)
as_total_ordering	When 'True', style the conjunction as a total ordering (e.g. x < y < z from (x < y) and (y < z))	None	None/False	('with_total_ordering_style',)

# 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	32, 8
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 23 operands: 10
9	Operation	operator: 23 operands: 11
10	ExprTuple	12, 27
11	ExprTuple	13, 14
12	Operation	operator: 16 operands: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 29 operand: 21
15	ExprTuple	21, 19
16	Literal
17	ExprTuple	21, 20
18	ExprTuple	21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	26, 25
23	Literal
24	ExprTuple	26, 27
25	Operation	operator: 29 operand: 31
26	Literal
27	Operation	operator: 29 operand: 32
28	ExprTuple	31
29	Literal
30	ExprTuple	32
31	Literal
32	Literal