Expression of type Lambda

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 Conditional, Lambda, t
from proveit.linear_algebra import Norm
from proveit.logic import And, CartExp, Equals, InSet
from proveit.numbers import Complex, NaturalPos, one
from proveit.physics.quantum.QPE import _psi_t_ket, two_pow_t

# build up the expression from sub-expressions
expr = Lambda(t, Conditional(And(InSet(_psi_t_ket, CartExp(Complex, two_pow_t)), Equals(Norm(_psi_t_ket), one)), InSet(t, 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())

t \mapsto \left\{\left(\lvert \psi_{t} \rangle \in \mathbb{C}^{2^{t}}\right) \land \left(\left \|\lvert \psi_{t} \rangle\right \| = 1\right) \textrm{ if } t \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: 29 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 10 operands: 6
4	Literal
5	ExprTuple	7, 8
6	ExprTuple	29, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Literal
10	Literal
11	ExprTuple	23, 14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operand: 23
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23
21	Literal
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	29
28	Literal
29	Variable