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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, 4, 5*  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
2instantiation76, 7, 6  ⊢  
  : , : , :
3instantiation76, 7, 8  ⊢  
  : , : , :
4instantiation24, 9, 10  ⊢  
  : , : , :
5instantiation11, 12  ⊢  
  :
6instantiation76, 14, 13  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
8instantiation76, 14, 15  ⊢  
  : , : , :
9instantiation46, 27, 16  ⊢  
  : , :
10instantiation17, 18, 19  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
12instantiation76, 53, 20  ⊢  
  : , : , :
13instantiation76, 22, 21  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
15instantiation76, 22, 23  ⊢  
  : , : , :
16instantiation24, 25, 26  ⊢  
  : , : , :
17axiom  ⊢  
 proveit.logic.equality.equals_transitivity
18instantiation36, 78, 28, 37, 30, 38, 27, 47, 48, 40  ⊢  
  : , : , : , : , : , :
19instantiation36, 37, 63, 28, 38, 29, 30, 41, 42, 47, 48, 40  ⊢  
  : , : , : , : , : , :
20instantiation31, 32, 73  ⊢  
  : , : , :
21instantiation76, 33, 73  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
23instantiation76, 33, 34  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
25instantiation46, 35, 40  ⊢  
  : , :
26instantiation36, 37, 63, 78, 38, 39, 47, 48, 40  ⊢  
  : , : , : , : , : , :
27instantiation46, 41, 42  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
29instantiation49  ⊢  
  : , :
30instantiation43  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
32instantiation44, 45  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
34theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
35instantiation46, 47, 48  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.multiplication.disassociation
37axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
38theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39instantiation49  ⊢  
  : , :
40instantiation76, 53, 50  ⊢  
  : , : , :
41instantiation76, 53, 51  ⊢  
  : , : , :
42instantiation76, 53, 52  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
44theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
46theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
47theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
48instantiation76, 53, 54  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
51instantiation76, 58, 55  ⊢  
  : , : , :
52instantiation76, 56, 57  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
54instantiation76, 58, 59  ⊢  
  : , : , :
55instantiation76, 61, 60  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
59instantiation76, 61, 62  ⊢  
  : , : , :
60instantiation76, 77, 63  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
62instantiation76, 64, 65  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
64instantiation66, 67, 68  ⊢  
  : , :
65assumption  ⊢  
66theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
67theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
68instantiation69, 70, 71  ⊢  
  : , :
69theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
70instantiation76, 72, 73  ⊢  
  : , : , :
71instantiation74, 75  ⊢  
  :
72theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
73theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
74theorem  ⊢  
 proveit.numbers.negation.int_closure
75instantiation76, 77, 78  ⊢  
  : , : , :
76theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
78theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements