Expression of type ExprTuple

from the theory of proveit.physics.quantum.QFT

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 Conditional, ExprTuple, Lambda, k, l, n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Exp, Interval, Mult, NaturalPos, Neg, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform

# build up the expression from sub-expressions
sub_expr1 = Exp(two, n)
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [k, l], instance_expr = Equals(Qmult(NumBra(l, n), InverseFourierTransform(n), NumKet(k, n)), Mult(frac(one, Exp(two, frac(n, two))), Exp(e, frac(Neg(Mult(two, pi, i, k, l)), sub_expr1)))), domain = Interval(zero, subtract(sub_expr1, one))), InSet(n, NaturalPos))))

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())

\left(n \mapsto \left\{\forall_{k, l \in \{0~\ldotp \ldotp~2^{n} - 1\}}~\left(\left({_{n}}\langle l \rvert \thinspace {\mathrm {FT}}^{\dag}_{n} \thinspace \lvert k \rangle_{n}\right) = \left(\frac{1}{2^{\frac{n}{2}}} \cdot \mathsf{e}^{\frac{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot l\right)}{2^{n}}}\right)\right) \textrm{ if } n \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 65 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 26 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	65, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	72, 73
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 67 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28, 29, 30
24	ExprTuple	31, 32
25	ExprTuple	72, 33
26	Literal
27	ExprTuple	73, 33
28	Operation	operator: 34 operands: 35
29	Operation	operator: 36 operand: 65
30	Operation	operator: 38 operands: 39
31	Operation	operator: 57 operands: 40
32	Operation	operator: 60 operands: 41
33	Operation	operator: 42 operands: 43
34	Literal
35	ExprTuple	73, 65
36	Literal
37	ExprTuple	65
38	Literal
39	ExprTuple	72, 65
40	ExprTuple	66, 44
41	ExprTuple	45, 46
42	Literal
43	ExprTuple	47, 48
44	Operation	operator: 60 operands: 49
45	Literal
46	Operation	operator: 57 operands: 50
47	Literal
48	Operation	operator: 51 operands: 52
49	ExprTuple	69, 53
50	ExprTuple	54, 55
51	Literal
52	ExprTuple	55, 56
53	Operation	operator: 57 operands: 58
54	Operation	operator: 62 operand: 64
55	Operation	operator: 60 operands: 61
56	Operation	operator: 62 operand: 66
57	Literal
58	ExprTuple	65, 69
59	ExprTuple	64
60	Literal
61	ExprTuple	69, 65
62	Literal
63	ExprTuple	66
64	Operation	operator: 67 operands: 68
65	Variable
66	Literal
67	Literal
68	ExprTuple	69, 70, 71, 72, 73
69	Literal
70	Literal
71	Literal
72	Variable
73	Variable