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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, , ,  ⊢  
  : , : , :
1reference8  ⊢  
2instantiation24, 11, 4, , ,  ⊢  
  : , :
3instantiation5, 6, 7, , ,  ⊢  
  : , : , :
4instantiation8, 9, 10, ,  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation15, 17, 58, 16, 13, 18, 11, 25, 26, 20, , ,  ⊢  
  : , : , : , : , : , :
7instantiation15, 16, 61, 58, 18, 12, 13, 21, 22, 25, 26, 20, , ,  ⊢  
  : , : , : , : , : , :
8theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
9instantiation24, 14, 20, ,  ⊢  
  : , :
10instantiation15, 16, 61, 17, 18, 19, 25, 26, 20, ,  ⊢  
  : , : , : , : , : , :
11instantiation24, 21, 22  ⊢  
  : , :
12instantiation27  ⊢  
  : , :
13instantiation23  ⊢  
  : , : , :
14instantiation24, 25, 26,  ⊢  
  : , :
15theorem  ⊢  
 proveit.numbers.multiplication.disassociation
16axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
17theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
18theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19instantiation27  ⊢  
  : , :
20instantiation59, 43, 28  ⊢  
  : , : , :
21instantiation29, 30, 31, 32  ⊢  
  : , :
22instantiation33, 34, 35  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
24theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
25instantiation59, 43, 36  ⊢  
  : , : , :
26instantiation59, 43, 37  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28assumption  ⊢  
29theorem  ⊢  
 proveit.numbers.division.div_complex_closure
30instantiation59, 43, 38  ⊢  
  : , : , :
31instantiation59, 43, 39  ⊢  
  : , : , :
32instantiation40, 41  ⊢  
  :
33theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
34instantiation59, 43, 42  ⊢  
  : , : , :
35instantiation59, 43, 44  ⊢  
  : , : , :
36instantiation59, 49, 45  ⊢  
  : , : , :
37instantiation59, 49, 46  ⊢  
  : , : , :
38instantiation59, 51, 47  ⊢  
  : , : , :
39instantiation59, 51, 48  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
41theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
42instantiation59, 49, 50  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
44instantiation59, 51, 52  ⊢  
  : , : , :
45assumption  ⊢  
46assumption  ⊢  
47instantiation59, 55, 53  ⊢  
  : , : , :
48instantiation59, 55, 54  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
50assumption  ⊢  
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
52instantiation59, 55, 56  ⊢  
  : , : , :
53instantiation59, 60, 57  ⊢  
  : , : , :
54instantiation59, 60, 58  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
56instantiation59, 60, 61  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
59theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
61theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2