In [1]:
import proveit
from proveit.physics.quantum.QPE import _phase_in_interval
theory = proveit.Theory() # the theorem's theory
In [2]:
%proving _phase_is_real
With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
_phase_is_real:
(see dependencies)
_phase_is_real:
(see dependencies)
In [3]:
# axiomatically:
_phase_in_interval
In [4]:
%qed
Out[4]:
| step type | requirements | statement | ||
|---|---|---|---|---|
| 0 | instantiation | 1, 2, 3, 4 | ⊢ | |
 :  ,  :  ,  :  | ||||
| 1 | conjecture | ⊢  | ||
| proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real | ||||
| 2 | conjecture | ⊢  | ||
| proveit.numbers.number_sets.real_numbers.zero_is_real | ||||
| 3 | instantiation | 9, 5, 6 | ⊢  | |
 :  ,  :  , : | ||||
| 4 | axiom | ⊢  | ||
| proveit.physics.quantum.QPE._phase_in_interval | ||||
| 5 | conjecture | ⊢  | ||
| proveit.numbers.number_sets.real_numbers.rational_within_real | ||||
| 6 | instantiation | 9, 7, 8 | ⊢  | |
:  , : , : | ||||
| 7 | conjecture | ⊢  | ||
| proveit.numbers.number_sets.rational_numbers.int_within_rational | ||||
| 8 | instantiation | 9, 10, 11 | ⊢  | |
:  , : , : | ||||
| 9 | theorem | ⊢  | ||
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset | ||||
| 10 | conjecture | ⊢  | ||
| proveit.numbers.number_sets.integers.nat_within_int | ||||
| 11 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.nat1 | ||||