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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  ⊢  
  : , : , :
1reference30  ⊢  
2instantiation26, 4  ⊢  
  : , : , :
3instantiation13, 41, 5, 6, 7*  ⊢  
  : , :
4instantiation26, 8  ⊢  
  : , : , :
5instantiation24, 47, 34  ⊢  
  : , :
6instantiation9, 58, 10  ⊢  
  : , :
7instantiation30, 11, 12  ⊢  
  : , : , :
8instantiation13, 55, 47, 22, 14*  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
10instantiation94, 15, 66  ⊢  
  : , : , :
11instantiation26, 16  ⊢  
  : , : , :
12instantiation17, 18  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.division.div_as_mult
14instantiation30, 19, 20  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
16instantiation21, 47, 43, 48, 22, 23*  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
18instantiation24, 47, 25  ⊢  
  : , :
19instantiation26, 27  ⊢  
  : , : , :
20instantiation28, 55, 54  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
22instantiation29, 96  ⊢  
  :
23instantiation30, 31, 32  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
25instantiation33, 34  ⊢  
  :
26axiom  ⊢  
 proveit.logic.equality.substitution
27instantiation35, 36, 93, 37*  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.multiplication.commutation
29theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30axiom  ⊢  
 proveit.logic.equality.equals_transitivity
31instantiation38, 51, 87, 89, 53, 52, 54, 55, 39  ⊢  
  : , : , : , : , : , :
32instantiation40, 87, 51, 52, 53, 54, 55, 41, 42*  ⊢  
  : , : , : , : , :
33theorem  ⊢  
 proveit.numbers.negation.complex_closure
34instantiation94, 64, 43  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
36instantiation94, 44, 45  ⊢  
  : , : , :
37instantiation46, 47  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.multiplication.disassociation
39instantiation94, 64, 48  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
41instantiation94, 64, 49  ⊢  
  : , : , :
42instantiation50, 87, 51, 52, 53, 54, 55  ⊢  
  : , : , : , :
43instantiation94, 71, 56  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
45instantiation94, 57, 58  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
47instantiation94, 64, 59  ⊢  
  : , : , :
48instantiation94, 71, 60  ⊢  
  : , : , :
49instantiation94, 71, 61  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
51axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
52instantiation62  ⊢  
  : , :
53theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
54instantiation94, 64, 63  ⊢  
  : , : , :
55instantiation94, 64, 65  ⊢  
  : , : , :
56instantiation94, 82, 66  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
58instantiation94, 67, 68  ⊢  
  : , : , :
59instantiation94, 71, 69  ⊢  
  : , : , :
60instantiation94, 78, 70  ⊢  
  : , : , :
61instantiation94, 78, 81  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63instantiation94, 71, 72  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
65instantiation73, 74, 86  ⊢  
  : , : , :
66instantiation75, 83, 76  ⊢  
  : , :
67theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
68instantiation94, 77, 96  ⊢  
  : , : , :
69instantiation94, 78, 79  ⊢  
  : , : , :
70instantiation80, 81  ⊢  
  :
71theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
72instantiation94, 82, 83  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
74instantiation84, 85  ⊢  
  : , :
75theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
76instantiation94, 95, 86  ⊢  
  : , : , :
77theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
78theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
79instantiation94, 88, 87  ⊢  
  : , : , :
80theorem  ⊢  
 proveit.numbers.negation.int_closure
81instantiation94, 88, 89  ⊢  
  : , : , :
82theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
83instantiation90, 91, 92  ⊢  
  : , :
84theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
85theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
86axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
87theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
88theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
89theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
90theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
91instantiation94, 95, 93  ⊢  
  : , : , :
92instantiation94, 95, 96  ⊢  
  : , : , :
93theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
94theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
95theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
96theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements