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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
0generalization1  ⊢  
1instantiation14, 2, 3,  ⊢  
  : , : , :
2instantiation4, 5,  ⊢  
  : , : , :
3instantiation14, 6, 7,  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 56, 20, 21, 8, 23, 29, 24, 25,  ⊢  
  : , : , : , : , : , :
6instantiation9, 21, 10, 20, 23, 11, 12, 29, 24, 25, 13, 28,  ⊢  
  : , : , : , : , : , :
7instantiation14, 15, 16,  ⊢  
  : , : , :
8instantiation31  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.addition.disassociation
10theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
11instantiation17  ⊢  
  : , : , :
12instantiation31  ⊢  
  : , :
13instantiation18, 25  ⊢  
  :
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation19, 20, 21, 56, 22, 23, 29, 24, 25, 28, 26,  ⊢  
  : , : , : , : , : , : , : , :
16instantiation27, 28, 29, 30,  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18theorem  ⊢  
 proveit.numbers.negation.complex_closure
19theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general
20theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
21axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
22instantiation31  ⊢  
  : , :
23theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24instantiation57, 35, 32  ⊢  
  : , : , :
25instantiation57, 35, 33  ⊢  
  : , : , :
26instantiation37  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_32
28instantiation57, 35, 34  ⊢  
  : , : , :
29instantiation57, 35, 36,  ⊢  
  : , : , :
30instantiation37  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32instantiation57, 42, 38  ⊢  
  : , : , :
33instantiation57, 42, 39  ⊢  
  : , : , :
34instantiation40, 41, 59  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
36instantiation57, 42, 43,  ⊢  
  : , : , :
37axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
38instantiation57, 47, 44  ⊢  
  : , : , :
39instantiation57, 47, 53  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
41instantiation45, 46  ⊢  
  : , :
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
43instantiation57, 47, 48,  ⊢  
  : , : , :
44instantiation49, 54  ⊢  
  :
45theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48instantiation57, 50, 51,  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.negation.int_closure
50instantiation52, 53, 54  ⊢  
  : , :
51assumption  ⊢  
52theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
53instantiation57, 55, 56  ⊢  
  : , : , :
54instantiation57, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
59assumption  ⊢