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.linear_algebra import LinMap
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex, Exp, NaturalPos, two
from proveit.physics.quantum import NumBra
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(NumBra(k, n), LinMap(CartExp(Complex, Exp(two, n)), Complex)), 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({_{n}}\langle k \rvert \in \mathcal{L}\left(\mathbb{C}^{2^{n}}, \mathbb{C}\right)\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: 42 body: 2
1	ExprTuple	42
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	42, 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, 42
22	Literal
23	ExprTuple	27, 34
24	Literal
25	ExprTuple	28, 29
26	Variable
27	Operation	operator: 30 operands: 31
28	Literal
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	35, 36
34	Literal
35	Operation	operator: 37 operands: 38
36	Operation	operator: 39 operand: 43
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43
41	Literal
42	Variable
43	Literal