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 b, l
from proveit.logic import Forall, NotEquals, Set
from proveit.numbers import Integer, frac, zero
from proveit.physics.quantum.QPE import _b_floor, _b_round, _delta_b, _two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [b, l], instance_expr = NotEquals(_delta_b, frac(l, _two_pow_t)), domains = [Set(_b_floor, _b_round), Integer], condition = NotEquals(l, zero))

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_{b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\}, l \in \mathbb{Z}~|~l \neq 0}~\left(\delta_{b} \neq \frac{l}{2^{t}}\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	parameters: 4 body: 5
4	ExprTuple	26, 29
5	Conditional	value: 6 condition: 7
6	Operation	operator: 23 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15
11	Operation	operator: 16 operand: 26
12	Operation	operator: 18 operands: 19
13	Operation	operator: 21 operands: 20
14	Operation	operator: 21 operands: 22
15	Operation	operator: 23 operands: 24
16	Literal
17	ExprTuple	26
18	Literal
19	ExprTuple	29, 25
20	ExprTuple	26, 27
21	Literal
22	ExprTuple	29, 28
23	Literal
24	ExprTuple	29, 30
25	Operation	operator: 31 operands: 32
26	Variable
27	Operation	operator: 33 operands: 34
28	Literal
29	Variable
30	Literal
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37, 38
35	Literal
36	Literal
37	Literal
38	Literal