In [1]:
import proveit
from proveit.physics.quantum.QPE import _t_in_natural_pos
theory = proveit.Theory() # the theorem's theory
In [2]:
%proving _two_pow_t_is_nat_pos
With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
_two_pow_t_is_nat_pos:
(see dependencies)
_two_pow_t_is_nat_pos:
(see dependencies)
In [3]:
# Recall that t (represented by the Literal t_)
# denotes the number of Qbits in the input register.
# Considered an axiom that t is a positive natural number
In [4]:
%qed
Out[4]:
| step type | requirements | statement | ||
|---|---|---|---|---|
| 0 | instantiation | 1, 2, 3 | ⊢ | |
 :  ,  :  | ||||
| 1 | conjecture | ⊢  | ||
| proveit.numbers.exponentiation.exp_natpos_closure | ||||
| 2 | conjecture | ⊢  | ||
| proveit.numbers.numerals.decimals.nat2 | ||||
| 3 | instantiation | 4, 5, 6 | ⊢  | |
 :  ,  :  ,  : | ||||
| 4 | theorem | ⊢  | ||
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset | ||||
| 5 | conjecture | ⊢  | ||
| proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat | ||||
| 6 | axiom | ⊢  | ||
| proveit.physics.quantum.QPE._t_in_natural_pos | ||||