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, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_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)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_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 \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\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: 46 body: 5
4	ExprTuple	46
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	46, 13
11	Operation	operator: 40 operands: 14
12	Literal
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 42 operands: 21
18	Operation	operator: 42 operands: 22
19	Literal
20	Operation	operator: 23 operands: 24
21	ExprTuple	26, 25
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	39, 28
25	Operation	operator: 40 operands: 29
26	Literal
27	Operation	operator: 31 operand: 34
28	Operation	operator: 31 operand: 35
29	ExprTuple	48, 44, 45, 33, 46
30	ExprTuple	34
31	Literal
32	ExprTuple	35
33	Literal
34	Operation	operator: 36 operands: 37
35	Literal
36	Literal
37	ExprTuple	38, 39
38	Operation	operator: 40 operands: 41
39	Operation	operator: 42 operands: 43
40	Literal
41	ExprTuple	48, 44, 45, 46, 47
42	Literal
43	ExprTuple	48, 49
44	Literal
45	Literal
46	Variable
47	Variable
48	Literal
49	Literal