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, , ,  ⊢  
  : , : , :
1reference18  ⊢  
2instantiation27, 4  ⊢  
  : , : , :
3instantiation18, 5, 6, , ,  ⊢  
  : , : , :
4instantiation7, 30, 54, 46, 8*  ⊢  
  : , :
5instantiation9, 77, 74, 10, 14, 50, 15, 16, , ,  ⊢  
  : , : , : , : , : , : , :
6instantiation11, 74, 77, 12, 13, 14, 50, 15, 16, 17*, , ,  ⊢  
  : , : , : , : , : , :
7theorem  ⊢  
 proveit.numbers.division.div_as_mult
8instantiation18, 19, 20  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.addition.leftward_commutation
10instantiation48  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.addition.association
12instantiation48  ⊢  
  : , :
13instantiation48  ⊢  
  : , :
14instantiation75, 62, 21  ⊢  
  : , : , :
15instantiation23, 54, 22  ⊢  
  : , :
16instantiation23, 31, 30  ⊢  
  : , :
17instantiation24, 25, 26*  ⊢  
  : , :
18axiom  ⊢  
 proveit.logic.equality.equals_transitivity
19instantiation27, 28  ⊢  
  : , : , :
20instantiation29, 30, 31  ⊢  
  : , :
21instantiation75, 55, 32  ⊢  
  : , : , :
22instantiation75, 62, 33  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
24theorem  ⊢  
 proveit.logic.equality.equals_reversal
25instantiation34, 35, 77, 74, 36, 37, 45, 50, 38*  ⊢  
  : , : , : , : , : , :
26theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
27axiom  ⊢  
 proveit.logic.equality.substitution
28instantiation39, 40, 41, 42*  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.multiplication.commutation
30instantiation75, 62, 43  ⊢  
  : , : , :
31instantiation44, 45, 54, 46  ⊢  
  : , :
32assumption  ⊢  
33instantiation75, 55, 47  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
35axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
36theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37instantiation48  ⊢  
  : , :
38instantiation49, 50  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
40instantiation75, 51, 52  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
42instantiation53, 54  ⊢  
  :
43instantiation75, 55, 56  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.division.div_complex_closure
45instantiation75, 62, 57  ⊢  
  : , : , :
46instantiation58, 71  ⊢  
  :
47assumption  ⊢  
48theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
49theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
50instantiation75, 62, 59  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
52instantiation75, 60, 61  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
54instantiation75, 62, 63  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
56assumption  ⊢  
57instantiation75, 67, 64  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
59assumption  ⊢  
60theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
61instantiation75, 65, 66  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
63instantiation75, 67, 68  ⊢  
  : , : , :
64instantiation75, 72, 69  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
66instantiation75, 70, 71  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
68instantiation75, 72, 73  ⊢  
  : , : , :
69instantiation75, 76, 74  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
71theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
72theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
73instantiation75, 76, 77  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
75theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
77theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements