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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.div_as_mult
2reference57  ⊢  
3instantiation6, 53, 19  ⊢  
  : , :
4instantiation7, 114, 8, 36, 9  ⊢  
  : , :
5instantiation15, 10, 11  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
7theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
8instantiation42  ⊢  
  : , :
9instantiation12, 19, 21  ⊢  
  :
10instantiation13, 14  ⊢  
  : , : , :
11instantiation15, 16, 17  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
13axiom  ⊢  
 proveit.logic.equality.substitution
14instantiation18, 53, 19, 39, 20, 21, 22*, 23*  ⊢  
  : , : , :
15axiom  ⊢  
 proveit.logic.equality.equals_transitivity
16instantiation24, 104, 114, 26, 28, 27, 57, 29, 30  ⊢  
  : , : , : , : , : , :
17instantiation25, 26, 114, 27, 28, 29, 30  ⊢  
  : , : , : , :
18theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_product
19instantiation112, 80, 31  ⊢  
  : , : , :
20instantiation55, 95  ⊢  
  :
21instantiation32, 33, 34  ⊢  
  : , :
22instantiation35, 36, 93, 37*  ⊢  
  : , :
23instantiation38, 45, 81, 39, 40, 41*  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.multiplication.disassociation
25theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
26axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
27theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28instantiation42  ⊢  
  : , :
29instantiation112, 80, 43  ⊢  
  : , : , :
30instantiation44, 45, 46  ⊢  
  : , :
31instantiation47, 60, 114  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
33instantiation112, 76, 48  ⊢  
  : , : , :
34instantiation112, 76, 49  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
36instantiation112, 50, 51  ⊢  
  : , : , :
37instantiation52, 53  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
39instantiation54, 67  ⊢  
  :
40instantiation55, 62  ⊢  
  :
41instantiation56, 69, 57, 58*  ⊢  
  : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43instantiation112, 91, 59  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
45instantiation112, 80, 60  ⊢  
  : , : , :
46instantiation112, 80, 61  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
48instantiation112, 89, 62  ⊢  
  : , : , :
49instantiation112, 89, 63  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
51instantiation112, 64, 65  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
53instantiation112, 80, 66  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.negation.real_closure
55theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
56theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
57instantiation112, 80, 67  ⊢  
  : , : , :
58instantiation68, 69  ⊢  
  :
59instantiation112, 70, 71  ⊢  
  : , : , :
60instantiation112, 91, 72  ⊢  
  : , : , :
61instantiation112, 91, 73  ⊢  
  : , : , :
62instantiation74, 85, 75  ⊢  
  :
63theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
64theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
65instantiation112, 76, 77  ⊢  
  : , : , :
66instantiation112, 91, 78  ⊢  
  : , : , :
67instantiation112, 91, 79  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
69instantiation112, 80, 81  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
71instantiation82, 83, 84  ⊢  
  : , :
72instantiation112, 100, 85  ⊢  
  : , : , :
73instantiation112, 100, 107  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
75instantiation86, 87, 88  ⊢  
  : , : , :
76theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
77instantiation112, 89, 95  ⊢  
  : , : , :
78instantiation112, 100, 90  ⊢  
  : , : , :
79instantiation112, 100, 102  ⊢  
  : , : , :
80theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
81instantiation112, 91, 92  ⊢  
  : , : , :
82theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
83instantiation112, 94, 93  ⊢  
  : , : , :
84instantiation112, 94, 95  ⊢  
  : , : , :
85instantiation112, 96, 98  ⊢  
  : , : , :
86theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
87theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
88instantiation97, 102, 103, 98  ⊢  
  : , : , :
89theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
90instantiation112, 113, 99  ⊢  
  : , : , :
91theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
92instantiation112, 100, 111  ⊢  
  : , : , :
93theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
94theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
95theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
96instantiation101, 102, 103  ⊢  
  : , :
97theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
98assumption  ⊢  
99theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
100theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
101theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
102instantiation112, 113, 104  ⊢  
  : , : , :
103instantiation105, 106, 107  ⊢  
  : , :
104theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
105theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
106instantiation112, 108, 109  ⊢  
  : , : , :
107instantiation110, 111  ⊢  
  :
108theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
109theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
110theorem  ⊢  
 proveit.numbers.negation.int_closure
111instantiation112, 113, 114  ⊢  
  : , : , :
112theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
113theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
114theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements