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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  ⊢  
  : , : , :
1reference6  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 10, 23  ⊢  
  : , :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation11, 12, 13, 41, 14, 15, 18, 16, 23  ⊢  
  : , : , : , : , : , :
8instantiation17, 23, 18, 19  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
10instantiation42, 28, 20  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.addition.disassociation
12axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
13theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
14theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15instantiation21  ⊢  
  : , :
16instantiation22, 23  ⊢  
  :
17theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_32
18instantiation42, 28, 24  ⊢  
  : , : , :
19instantiation25  ⊢  
  :
20instantiation26, 27, 44  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22theorem  ⊢  
 proveit.numbers.negation.complex_closure
23instantiation42, 28, 29  ⊢  
  : , : , :
24instantiation42, 33, 30  ⊢  
  : , : , :
25axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
26theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
27instantiation31, 32  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
29instantiation42, 33, 34  ⊢  
  : , : , :
30instantiation42, 36, 35  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
34instantiation42, 36, 37  ⊢  
  : , : , :
35instantiation38, 39  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
37instantiation42, 40, 41  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.negation.int_closure
39instantiation42, 43, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
41theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
42theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
44assumption  ⊢