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
from proveit.logic import Forall, InSet, Set
from proveit.numbers import IntervalOO, Mult, Neg, one
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], instance_expr = InSet(Mult(_two_pow_t, _delta_b), IntervalOO(Neg(one), one)), domain = Set(_b_floor, _b_round))

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\}}~\left(\left(2^{t} \cdot \delta_{b}\right) \in \left(-1,1\right)\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: 32 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 8 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	32, 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 33
17	Literal
18	ExprTuple	22, 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 26 operand: 32
21	Operation	operator: 28 operand: 33
22	Literal
23	Literal
24	Literal
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	32
28	Literal
29	ExprTuple	33
30	Literal
31	Literal
32	Variable
33	Literal