logo

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, 4  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
2instantiation6, 18, 7, 48, 19, 8, 20, 21, 5  ⊢  
  : , : , : , : , : , :
3instantiation6, 7, 18, 8, 9, 19, 20, 21, 24, 10  ⊢  
  : , : , : , : , : , :
4instantiation11, 12, 13  ⊢  
  : , : , :
5instantiation49, 29, 14  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.addition.disassociation
7theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
8instantiation15  ⊢  
  : , :
9instantiation15  ⊢  
  : , :
10instantiation16, 21  ⊢  
  :
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation17, 48, 18, 19, 20, 21, 24, 22  ⊢  
  : , : , : , : , : , : , : , :
13instantiation23, 24, 25  ⊢  
  : , :
14instantiation49, 34, 26  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16theorem  ⊢  
 proveit.numbers.negation.complex_closure
17theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general
18axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
19theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20instantiation49, 29, 27  ⊢  
  : , : , :
21instantiation49, 29, 28  ⊢  
  : , : , :
22instantiation31  ⊢  
  :
23theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_reverse
24instantiation49, 29, 30  ⊢  
  : , : , :
25instantiation31  ⊢  
  :
26instantiation49, 41, 32  ⊢  
  : , : , :
27instantiation49, 34, 33  ⊢  
  : , : , :
28instantiation49, 34, 35  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
30instantiation36, 37, 51  ⊢  
  : , : , :
31axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
32instantiation38, 46, 39  ⊢  
  : , :
33instantiation49, 41, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation49, 41, 44  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
37instantiation42, 43  ⊢  
  : , :
38theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
39instantiation45, 44  ⊢  
  :
40instantiation45, 46  ⊢  
  :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
44instantiation49, 47, 48  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.negation.int_closure
46instantiation49, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
49theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
51assumption  ⊢