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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  ⊢  
  : , :
1reference33  ⊢  
2instantiation60, 43, 4  ⊢  
  : , : , :
3instantiation12, 5, 6  ⊢  
  : , : , :
4instantiation60, 40, 7  ⊢  
  : , : , :
5instantiation27, 15, 8  ⊢  
  : , :
6instantiation9, 10, 11  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
8instantiation12, 13, 14  ⊢  
  : , : , :
9axiom  ⊢  
 proveit.logic.equality.equals_transitivity
10instantiation20, 62, 16, 21, 18, 22, 15, 28, 29, 24  ⊢  
  : , : , : , : , : , :
11instantiation20, 21, 52, 16, 22, 17, 18, 34, 25, 28, 29, 24  ⊢  
  : , : , : , : , : , :
12theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
13instantiation27, 19, 24  ⊢  
  : , :
14instantiation20, 21, 52, 62, 22, 23, 28, 29, 24  ⊢  
  : , : , : , : , : , :
15instantiation27, 34, 25  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
17instantiation30  ⊢  
  : , :
18instantiation26  ⊢  
  : , : , :
19instantiation27, 28, 29  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.multiplication.disassociation
21axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
22theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23instantiation30  ⊢  
  : , :
24instantiation60, 43, 31  ⊢  
  : , : , :
25instantiation60, 43, 32  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
27theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
29instantiation33, 34, 35  ⊢  
  : , :
30theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31instantiation36, 37, 38, 39  ⊢  
  : , : , :
32instantiation60, 40, 41  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
34instantiation60, 43, 42  ⊢  
  : , : , :
35instantiation60, 43, 44  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
38instantiation60, 47, 45  ⊢  
  : , : , :
39axiom  ⊢  
 proveit.physics.quantum.QPE._phase_in_interval
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42instantiation60, 47, 46  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
44instantiation60, 47, 48  ⊢  
  : , : , :
45instantiation60, 50, 59  ⊢  
  : , : , :
46instantiation60, 50, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
48instantiation60, 50, 51  ⊢  
  : , : , :
49instantiation60, 61, 52  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51instantiation53, 54, 55  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
53theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
54instantiation60, 56, 57  ⊢  
  : , : , :
55instantiation58, 59  ⊢  
  :
56theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
57assumption  ⊢  
58theorem  ⊢  
 proveit.numbers.negation.int_closure
59instantiation60, 61, 62  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1