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, LessEq, Neg, one
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Neg(Add(e, one))
sub_expr2 = Add(Neg(_two_pow__t_minus_one), one)
expr = And(LessEq(sub_expr2, sub_expr2), LessEq(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(-2^{t - 1} + 1\right)\right) \land \left(\left(-2^{t - 1} + 1\right) \leq \left(-\left(e + 1\right)\right)\right) \land \left(\left(-\left(e + 1\right)\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: 8 operands: 6
4	Operation	operator: 8 operands: 7
5	Operation	operator: 8 operands: 9
6	ExprTuple	10, 10
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	11, 18
10	Operation	operator: 24 operands: 12
11	Operation	operator: 28 operand: 15
12	ExprTuple	14, 30
13	ExprTuple	15
14	Operation	operator: 28 operand: 18
15	Operation	operator: 24 operands: 17
16	ExprTuple	18
17	ExprTuple	19, 30
18	Operation	operator: 20 operands: 21
19	Variable
20	Literal
21	ExprTuple	22, 23
22	Literal
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Operation	operator: 28 operand: 30
28	Literal
29	ExprTuple	30
30	Literal