Expression of type Or

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, l
from proveit.logic import Or
from proveit.numbers import Add, Less, Neg, one
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
expr = Or(Less(l, Add(Neg(_two_pow__t_minus_one), one)), Less(Neg(Add(e, one)), l))

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(l < \left(-2^{t - 1} + 1\right)\right) \lor \left(\left(-\left(e + 1\right)\right) < l\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',)

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