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, m
from proveit.logic import Forall, InSet
from proveit.numbers import Complex, Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _phase, _t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [k], instance_expr = InSet(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Qmult(NumBra(m, _t), InverseFourierTransform(_t), NumKet(k, _t))), Complex), domain = _m_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_{k \in \{0~\ldotp \ldotp~2^{t} - 1\}}~\left(\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \lvert k \rangle_{t}\right)\right) \in \mathbb{C}\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: 49 body: 5
4	ExprTuple	49
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	49, 13
11	Operation	operator: 33 operands: 14
12	Literal
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 41 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Operation	operator: 24 operands: 25
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28, 29, 30
24	Literal
25	ExprTuple	31, 32
26	Literal
27	Operation	operator: 33 operands: 34
28	Operation	operator: 35 operands: 36
29	Operation	operator: 37 operand: 51
30	Operation	operator: 39 operands: 40
31	Operation	operator: 41 operands: 42
32	Operation	operator: 43 operand: 52
33	Literal
34	ExprTuple	50, 45, 46, 47, 49
35	Literal
36	ExprTuple	48, 51
37	Literal
38	ExprTuple	51
39	Literal
40	ExprTuple	49, 51
41	Literal
42	ExprTuple	50, 51
43	Literal
44	ExprTuple	52
45	Literal
46	Literal
47	Literal
48	Variable
49	Variable
50	Literal
51	Literal
52	Literal