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 Equals, Forall
from proveit.numbers import Exp, Mod, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [k], instance_expr = Equals(Exp(e, Neg(frac(Mult(two, pi, i, k, Mod(m, _two_pow_t)), _two_pow_t))), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))), 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(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \left(m ~\textup{mod}~ 2^{t}\right)}{2^{t}}} = \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\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: 45 body: 5
4	ExprTuple	45
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	45, 14
12	Operation	operator: 50 operands: 15
13	Operation	operator: 50 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	20, 19
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22, 23
19	Operation	operator: 34 operand: 28
20	Literal
21	Operation	operator: 34 operand: 29
22	Literal
23	Operation	operator: 26 operands: 27
24	ExprTuple	28
25	ExprTuple	29
26	Literal
27	ExprTuple	49, 30
28	Operation	operator: 32 operands: 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operand: 38
31	ExprTuple	36, 49
32	Literal
33	ExprTuple	37, 49
34	Literal
35	ExprTuple	38
36	Operation	operator: 40 operands: 39
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	52, 43, 44, 45, 42
40	Literal
41	ExprTuple	52, 43, 44, 45, 48
42	Operation	operator: 46 operands: 47
43	Literal
44	Literal
45	Variable
46	Literal
47	ExprTuple	48, 49
48	Variable
49	Operation	operator: 50 operands: 51
50	Literal
51	ExprTuple	52, 53
52	Literal
53	Literal