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 import e
from proveit.logic import And
from proveit.numbers import Add, Less, LessEq, Neg, one
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Add(e, one)
sub_expr2 = Neg(sub_expr1)
expr = And(LessEq(Add(Neg(_two_pow__t_minus_one), one), sub_expr2), Less(sub_expr2, sub_expr1), LessEq(sub_expr1, _two_pow__t_minus_one))

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(\left(-2^{t - 1} + 1\right) \leq \left(-\left(e + 1\right)\right)\right) \land \left(\left(-\left(e + 1\right)\right) < \left(e + 1\right)\right) \land \left(\left(e + 1\right) \leq 2^{t - 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',)
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, 5
3	Operation	operator: 9 operands: 6
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	ExprTuple	11, 12
7	Literal
8	ExprTuple	12, 16
9	Literal
10	ExprTuple	16, 19
11	Operation	operator: 25 operands: 13
12	Operation	operator: 29 operand: 16
13	ExprTuple	15, 31
14	ExprTuple	16
15	Operation	operator: 29 operand: 19
16	Operation	operator: 25 operands: 18
17	ExprTuple	19
18	ExprTuple	20, 31
19	Operation	operator: 21 operands: 22
20	Variable
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