Expression of type Forall

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 m
from proveit.logic import Forall
from proveit.numbers import Exp, LessEq, ModAbs, one, subtract, two
from proveit.physics.quantum.QPE import _b_floor, _m_domain, _n, _success_cond, _t, _two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m], instance_expr = _success_cond, domain = _m_domain, condition = LessEq(ModAbs(subtract(m, _b_floor), _two_pow_t), subtract(Exp(two, subtract(_t, _n)), 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())

\forall_{m \in \{0~\ldotp \ldotp~2^{t} - 1\}~|~\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} \leq \left(2^{t - n} - 1\right)}~\left(\left|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1} \leq 2^{-n}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 46 body: 5
4	ExprTuple	46
5	Conditional	value: 6 condition: 7
6	Operation	operator: 19 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 28 operands: 15
12	Operation	operator: 49 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21, 56
16	ExprTuple	55, 59
17	Literal
18	ExprTuple	46, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 53 operands: 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 53 operands: 30
25	ExprTuple	31, 32
26	Literal
27	ExprTuple	33, 34
28	Literal
29	ExprTuple	35, 44
30	ExprTuple	36, 45
31	Operation	operator: 37 operands: 38
32	Operation	operator: 60 operand: 43
33	Literal
34	Operation	operator: 53 operands: 40
35	Operation	operator: 53 operands: 41
36	Operation	operator: 49 operands: 42
37	Literal
38	ExprTuple	46, 44
39	ExprTuple	43
40	ExprTuple	44, 45
41	ExprTuple	46, 47
42	ExprTuple	55, 48
43	Literal
44	Operation	operator: 49 operands: 50
45	Operation	operator: 60 operand: 56
46	Variable
47	Operation	operator: 60 operand: 57
48	Operation	operator: 53 operands: 54
49	Literal
50	ExprTuple	55, 58
51	ExprTuple	56
52	ExprTuple	57
53	Literal
54	ExprTuple	58, 59
55	Literal
56	Literal
57	Literal
58	Literal
59	Operation	operator: 60 operand: 62
60	Literal
61	ExprTuple	62
62	Literal