Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

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, Lambda, k, n
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex, Exp, NaturalPos, two
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [k], instance_expr = InSet(NumKet(k, n), CartExp(Complex, Exp(two, n))), domain = n_bit_interval), 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())

n \mapsto \left\{\forall_{k \in \{0~\ldotp \ldotp~2^{n} - 1\}}~\left(\lvert k \rangle_{n} \in \mathbb{C}^{2^{n}}\right) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 39 body: 2
1	ExprTuple	39
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 15 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	39, 9
8	Lambda	parameter: 26 body: 11
9	Literal
10	ExprTuple	26
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	26, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	ExprTuple	26, 39
22	Literal
23	ExprTuple	27, 32
24	Literal
25	ExprTuple	28, 29
26	Variable
27	Literal
28	Literal
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operand: 40
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40
38	Literal
39	Variable
40	Literal