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 k, t
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, QubitSpace, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [k], instance_expr = InSet(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), TensorProd(ket1, NumKet(k, t))), TensorProd(QubitSpace, CartExp(Complex, two_pow_t))), domain = Interval(zero, subtract(two_pow_t, one)))

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_{k \in \{0~\ldotp \ldotp~2^{t} - 1\}}~\left(\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right)\right) \in \left(\mathbb{C}^{2} {\otimes} \mathbb{C}^{2^{t}}\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: 52 body: 5
4	ExprTuple	52
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	52, 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 26 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	ExprTuple	19, 20
16	ExprTuple	21, 22
17	Literal
18	ExprTuple	23, 24
19	Operation	operator: 45 operands: 25
20	Operation	operator: 26 operands: 27
21	Operation	operator: 29 operands: 28
22	Operation	operator: 29 operands: 30
23	Literal
24	Operation	operator: 31 operands: 32
25	ExprTuple	33, 34
26	Literal
27	ExprTuple	35, 36
28	ExprTuple	37, 53
29	Literal
30	ExprTuple	37, 38
31	Literal
32	ExprTuple	38, 39
33	Literal
34	Operation	operator: 40 operands: 41
35	Operation	operator: 42 operand: 55
36	Operation	operator: 43 operands: 44
37	Literal
38	Operation	operator: 45 operands: 46
39	Operation	operator: 47 operand: 55
40	Literal
41	ExprTuple	53, 49, 50, 51, 52
42	Literal
43	Literal
44	ExprTuple	52, 54
45	Literal
46	ExprTuple	53, 54
47	Literal
48	ExprTuple	55
49	Literal
50	Literal
51	Literal
52	Variable
53	Literal
54	Variable
55	Literal