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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 34, 41, 11, 13, 12, 5, 14, 15  ⊢  
  : , : , : , : , : , :
3instantiation6, 11, 41, 12, 13, 9, 14, 15, 7*  ⊢  
  : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.multiplication.disassociation
5instantiation8, 9  ⊢  
  :
6theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
7instantiation10, 11, 41, 12, 13, 14, 15  ⊢  
  : , : , : , :
8theorem  ⊢  
 proveit.numbers.negation.complex_closure
9instantiation39, 24, 16  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
11axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
12theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13instantiation17  ⊢  
  : , :
14instantiation18, 19, 20  ⊢  
  : , :
15instantiation39, 24, 21  ⊢  
  : , : , :
16instantiation39, 29, 22  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
19instantiation39, 24, 23  ⊢  
  : , : , :
20instantiation39, 24, 25  ⊢  
  : , : , :
21instantiation26, 27  ⊢  
  :
22instantiation39, 35, 28  ⊢  
  : , : , :
23instantiation39, 29, 30  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
25instantiation31, 32, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
27theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
28instantiation39, 40, 34  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
30instantiation39, 35, 36  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
32instantiation37, 38  ⊢  
  : , :
33axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
34theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
36instantiation39, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
39theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
41theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements