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  ⊢  
  : , : , :
1reference9  ⊢  
2instantiation3, 18, 27, 4, 5*  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_as_mult
4instantiation6, 67  ⊢  
  :
5instantiation11, 7, 8  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
7instantiation9, 10  ⊢  
  : , : , :
8instantiation11, 12, 13  ⊢  
  : , : , :
9axiom  ⊢  
 proveit.logic.equality.substitution
10instantiation14, 15, 64, 16*  ⊢  
  : , :
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation17, 18, 33  ⊢  
  : , :
13instantiation19, 60, 58, 20, 21, 22, 33, 29, 30, 23*  ⊢  
  : , : , : , : , : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
15instantiation65, 24, 25  ⊢  
  : , : , :
16instantiation26, 27  ⊢  
  :
17theorem  ⊢  
 proveit.numbers.multiplication.commutation
18instantiation28, 29, 30  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
20axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
21instantiation31  ⊢  
  : , :
22theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23instantiation32, 33  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
25instantiation65, 34, 35  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
27instantiation65, 39, 36  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
29instantiation65, 39, 37  ⊢  
  : , : , :
30instantiation65, 39, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
33instantiation65, 39, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
35instantiation65, 41, 42  ⊢  
  : , : , :
36instantiation65, 48, 43  ⊢  
  : , : , :
37instantiation44, 45, 46  ⊢  
  : , : , :
38instantiation65, 48, 47  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
40instantiation65, 48, 49  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
42instantiation65, 50, 67  ⊢  
  : , : , :
43instantiation65, 54, 51  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
45instantiation52, 53  ⊢  
  : , :
46assumption  ⊢  
47instantiation65, 54, 55  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
49instantiation65, 56, 57  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
51instantiation65, 59, 58  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
54theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
55instantiation65, 59, 60  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
57instantiation61, 62, 63  ⊢  
  : , :
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
61theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
62instantiation65, 66, 64  ⊢  
  : , : , :
63instantiation65, 66, 67  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
65theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
67theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements