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 l
from proveit.logic import Forall, InSet
from proveit.numbers import Complex, Exp, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = InSet(frac(one, Exp(_diff_l_scaled_delta_floor, two)), Complex), domain = _neg_domain)

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_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}}~\left(\frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \in \mathbb{C}\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: 30 body: 5
4	ExprTuple	30
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	30, 13
11	Operation	operator: 14 operands: 15
12	Literal
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	54, 18
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 45 operands: 21
19	Operation	operator: 40 operands: 22
20	Operation	operator: 49 operand: 26
21	ExprTuple	24, 51
22	ExprTuple	25, 54
23	ExprTuple	26
24	Operation	operator: 40 operands: 27
25	Operation	operator: 49 operand: 32
26	Operation	operator: 40 operands: 29
27	ExprTuple	30, 31
28	ExprTuple	32
29	ExprTuple	33, 54
30	Variable
31	Operation	operator: 49 operand: 36
32	Operation	operator: 45 operands: 35
33	Variable
34	ExprTuple	36
35	ExprTuple	51, 37
36	Operation	operator: 38 operands: 39
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	52, 44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operand: 53
44	Operation	operator: 49 operand: 54
45	Literal
46	ExprTuple	51, 52
47	Literal
48	ExprTuple	53
49	Literal
50	ExprTuple	54
51	Literal
52	Literal
53	Literal
54	Literal