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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  ⊢  
  : , : , :
1reference16  ⊢  
2instantiation25, 4  ⊢  
  : , : , :
3instantiation25, 5  ⊢  
  : , : , :
4instantiation10, 19, 43, 11, 6*  ⊢  
  : , :
5instantiation25, 7  ⊢  
  : , : , :
6instantiation16, 8, 9  ⊢  
  : , : , :
7instantiation10, 29, 43, 11, 12*  ⊢  
  : , :
8instantiation25, 26  ⊢  
  : , : , :
9instantiation16, 13, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.division.div_as_mult
11instantiation15, 71  ⊢  
  :
12instantiation16, 17, 18  ⊢  
  : , : , :
13instantiation27, 19, 33  ⊢  
  : , :
14instantiation20, 62, 74, 21, 22, 23, 33, 29, 30, 24*  ⊢  
  : , : , : , : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
16axiom  ⊢  
 proveit.logic.equality.equals_transitivity
17instantiation25, 26  ⊢  
  : , : , :
18instantiation27, 29, 33  ⊢  
  : , :
19instantiation28, 29, 30  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
21axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
22instantiation31  ⊢  
  : , :
23theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24instantiation32, 33  ⊢  
  :
25axiom  ⊢  
 proveit.logic.equality.substitution
26instantiation34, 35, 69, 36*  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.multiplication.commutation
28theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
29instantiation72, 51, 37  ⊢  
  : , : , :
30instantiation72, 51, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
33instantiation72, 51, 39  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
35instantiation72, 40, 41  ⊢  
  : , : , :
36instantiation42, 43  ⊢  
  :
37instantiation44, 45, 46  ⊢  
  : , : , :
38instantiation72, 60, 47  ⊢  
  : , : , :
39instantiation72, 60, 48  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
41instantiation72, 49, 50  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
43instantiation72, 51, 52  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
45instantiation53, 54  ⊢  
  : , :
46assumption  ⊢  
47instantiation72, 67, 55  ⊢  
  : , : , :
48instantiation72, 56, 57  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
50instantiation72, 58, 59  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
52instantiation72, 60, 61  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
55instantiation72, 73, 62  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
57instantiation63, 64, 65  ⊢  
  : , :
58theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
59instantiation72, 66, 71  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
61instantiation72, 67, 68  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
63theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
64instantiation72, 70, 69  ⊢  
  : , : , :
65instantiation72, 70, 71  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
67theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
68instantiation72, 73, 74  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
70theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
71theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
72theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
73theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements