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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 12, 11, 35, 14, 13, 15, 16, 5  ⊢  
  : , : , : , : , : , :
3instantiation6, 11, 12, 13, 14, 15, 16, 9, 7*  ⊢  
  : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.multiplication.disassociation
5instantiation8, 9  ⊢  
  :
6theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
7instantiation10, 11, 12, 13, 14, 15, 16  ⊢  
  : , : , : , :
8theorem  ⊢  
 proveit.numbers.negation.complex_closure
9instantiation40, 20, 17  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
11theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
12axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
13instantiation18  ⊢  
  : , :
14theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15instantiation40, 20, 19  ⊢  
  : , : , :
16instantiation40, 20, 21  ⊢  
  : , : , :
17instantiation40, 23, 22  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19instantiation40, 23, 24  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
21instantiation25, 26, 27  ⊢  
  : , : , :
22instantiation40, 28, 29  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
24instantiation40, 30, 31  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
26instantiation32, 33  ⊢  
  : , :
27assumption  ⊢  
28theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
29instantiation40, 34, 35  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
31instantiation36, 37, 38  ⊢  
  : , :
32theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
34theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
35theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
36theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
37instantiation40, 41, 39  ⊢  
  : , : , :
38instantiation40, 41, 42  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
40theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
42theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements