logo

Show the Proof

In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0instantiation1, 2, 3  ⊢  
  : , : , :
1reference37  ⊢  
2reference38  ⊢  
3instantiation4, 5  ⊢  
  :
4theorem  ⊢  
 proveit.trigonometry.real_closure
5instantiation6, 7, 8  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
7instantiation19, 9, 23  ⊢  
  : , :
8instantiation10, 11, 12, 13, 14, 15, 16, 17, 18  ⊢  
  : , : , : , : , : , :
9instantiation19, 21, 22  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.multiplication.disassociation
11axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
12theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
13theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
14theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15instantiation20  ⊢  
  : , :
16instantiation37, 38, 21  ⊢  
  : , : , :
17instantiation37, 38, 22  ⊢  
  : , : , :
18instantiation37, 38, 23  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
20theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21instantiation24, 25, 26  ⊢  
  : , : , :
22instantiation37, 28, 27  ⊢  
  : , : , :
23instantiation37, 28, 29  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
25instantiation30, 31  ⊢  
  : , :
26theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
29instantiation32, 33  ⊢  
  :
30theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
32theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
33instantiation34, 35, 36  ⊢  
  :
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
35instantiation37, 38, 39  ⊢  
  : , : , :
36assumption  ⊢  
37theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
39instantiation40, 41  ⊢  
  :
40theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
41theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int