Expression of type Implies

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 And, Implies, InSet, Union
from proveit.numbers import ModAbs, greater, greater_eq, zero
from proveit.physics.quantum.QPE import _neg_domain, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Implies(greater_eq(l, zero), And(InSet(l, Union(_neg_domain, _pos_domain)), greater(ModAbs(l, _two_pow_t), e)))

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 \geq 0\right) \Rightarrow \left(\left(l \in \left(\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right)\right) \land \left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\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',)
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: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 24
7	Literal
8	ExprTuple	10, 11
9	Literal
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	24, 16
14	Literal
15	ExprTuple	39, 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 27 operands: 26
23	Operation	operator: 27 operands: 28
24	Variable
25	Operation	operator: 40 operands: 29
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	35, 38
29	ExprTuple	42, 46
30	Operation	operator: 44 operands: 32
31	Operation	operator: 48 operand: 35
32	ExprTuple	34, 50
33	ExprTuple	35
34	Operation	operator: 48 operand: 38
35	Operation	operator: 44 operands: 37
36	ExprTuple	38
37	ExprTuple	39, 50
38	Operation	operator: 40 operands: 41
39	Variable
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Literal