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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
2instantiation5, 49, 7, 6, 10, 8, 4, 11, 12, 13  ⊢  
  : , : , : , : , : , :
3instantiation5, 6, 44, 7, 8, 9, 10, 15, 16, 11, 12, 13  ⊢  
  : , : , : , : , : , :
4instantiation14, 15, 16  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.multiplication.disassociation
6axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
7theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
8theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9instantiation17  ⊢  
  : , :
10instantiation18  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
12instantiation47, 22, 19  ⊢  
  : , : , :
13instantiation47, 22, 20  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
15instantiation47, 22, 21  ⊢  
  : , : , :
16instantiation47, 22, 23  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
19theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
20instantiation47, 25, 24  ⊢  
  : , : , :
21instantiation47, 25, 26  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
23instantiation47, 27, 28  ⊢  
  : , : , :
24instantiation47, 30, 29  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
26instantiation47, 30, 40  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
29instantiation47, 31, 32  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
31instantiation33, 34, 35  ⊢  
  : , :
32assumption  ⊢  
33theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
34theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
35instantiation36, 37, 38  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
37instantiation39, 40, 41  ⊢  
  : , :
38instantiation42, 43  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
40instantiation47, 48, 44  ⊢  
  : , : , :
41instantiation47, 45, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.negation.int_closure
43instantiation47, 48, 49  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
45theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
46axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1