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 Norm, ScalarMult, VecAdd
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# 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 = Equals(Norm(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), one), 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(\left \|\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right \| = 1\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: 61 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 48
9	Literal
10	ExprTuple	61, 12
11	Operation	operator: 13 operand: 17
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	18, 38
17	Operation	operator: 35 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 48
22	Operation	operator: 41 operands: 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 59 operand: 32
25	ExprTuple	48, 29
26	Literal
27	ExprTuple	30, 31
28	ExprTuple	32
29	Operation	operator: 55 operands: 33
30	Operation	operator: 44 operand: 38
31	Operation	operator: 35 operands: 36
32	Variable
33	ExprTuple	57, 37
34	ExprTuple	38
35	Literal
36	ExprTuple	39, 40
37	Operation	operator: 41 operands: 42
38	Literal
39	Operation	operator: 55 operands: 43
40	Operation	operator: 44 operand: 48
41	Literal
42	ExprTuple	48, 57
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	48
46	Literal
47	Operation	operator: 49 operands: 50
48	Literal
49	Literal
50	ExprTuple	57, 51, 52, 53, 54
51	Literal
52	Literal
53	Operation	operator: 55 operands: 56
54	Literal
55	Literal
56	ExprTuple	57, 58
57	Literal
58	Operation	operator: 59 operand: 61
59	Literal
60	ExprTuple	61
61	Variable