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
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
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)), NumKet(k, t)), 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 \lvert k \rangle_{t}\right) \in \mathbb{C}^{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: 43 body: 5
4	ExprTuple	43
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	43, 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	22, 32
18	Literal
19	ExprTuple	23, 24
20	Operation	operator: 36 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Literal
24	Operation	operator: 28 operands: 29
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	43, 45
28	Literal
29	ExprTuple	32, 33
30	Literal
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operand: 46
34	Literal
35	ExprTuple	44, 40, 41, 42, 43
36	Literal
37	ExprTuple	44, 45
38	Literal
39	ExprTuple	46
40	Literal
41	Literal
42	Literal
43	Variable
44	Literal
45	Variable
46	Literal