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 Variable, t
from proveit.linear_algebra import MatrixExp, Unitary
from proveit.logic import Forall, InSet
from proveit.numbers import Add, Exp, Interval, Neg, one, two, zero
from proveit.physics.quantum.QPE import _U, _s

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [sub_expr1], instance_expr = InSet(MatrixExp(_U, Exp(two, Neg(sub_expr1))), Unitary(Exp(two, _s))), domain = Interval(Add(Neg(t), one), 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_{{_{-}a} \in \{-t + 1~\ldotp \ldotp~0\}}~\left(U^{2^{-{_{-}a}}} \in \textrm{U}\left(2^{s}\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: 37 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	37, 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operand: 21
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21
17	Literal
18	ExprTuple	22, 23
19	Literal
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	ExprTuple	30, 29
25	Literal
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	32, 33
29	Operation	operator: 35 operand: 37
30	Literal
31	Literal
32	Operation	operator: 35 operand: 38
33	Literal
34	ExprTuple	37
35	Literal
36	ExprTuple	38
37	Variable
38	Variable