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 Exp, Real, frac, one, two
from proveit.physics.quantum.QPE import _neg_domain

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = InSet(frac(one, Exp(l, two)), Real), 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}{l^{2}} \in \mathbb{R}\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: 24 body: 5
4	ExprTuple	24
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	24, 13
11	Operation	operator: 14 operands: 15
12	Literal
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	41, 18
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 31 operands: 21
19	Operation	operator: 35 operands: 22
20	Operation	operator: 39 operand: 26
21	ExprTuple	24, 33
22	ExprTuple	25, 41
23	ExprTuple	26
24	Variable
25	Operation	operator: 39 operand: 29
26	Operation	operator: 35 operands: 28
27	ExprTuple	29
28	ExprTuple	30, 41
29	Operation	operator: 31 operands: 32
30	Variable
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal