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  ⊢  
  : , : , :
1reference6  ⊢  
2instantiation11, 4  ⊢  
  : , : , :
3instantiation13, 5  ⊢  
  : , :
4instantiation6, 7, 8  ⊢  
  : , : , :
5instantiation9, 33, 10  ⊢  
  : , :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation11, 12  ⊢  
  : , : , :
8instantiation13, 14  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
10instantiation15, 21, 35, 16  ⊢  
  : , :
11axiom  ⊢  
 proveit.logic.equality.substitution
12instantiation17, 50, 18, 51, 52, 19, 59, 60, 54, 21  ⊢  
  : , : , : , : , : , :
13theorem  ⊢  
 proveit.logic.equality.equals_reversal
14instantiation20, 33, 21, 22, 23, 24*, 25*  ⊢  
  : , : , : , :
15theorem  ⊢  
 proveit.numbers.division.div_complex_closure
16instantiation26, 67  ⊢  
  :
17theorem  ⊢  
 proveit.numbers.multiplication.association
18theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
19instantiation27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
21instantiation74, 64, 28  ⊢  
  : , : , :
22instantiation74, 30, 29  ⊢  
  : , : , :
23instantiation74, 30, 31  ⊢  
  : , : , :
24instantiation32, 33  ⊢  
  :
25instantiation34, 35  ⊢  
  :
26theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
28instantiation74, 68, 36  ⊢  
  : , : , :
29instantiation74, 38, 37  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
31instantiation74, 38, 39  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.division.frac_one_denom
33instantiation40, 41, 42  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
35instantiation74, 64, 43  ⊢  
  : , : , :
36instantiation74, 72, 44  ⊢  
  : , : , :
37instantiation74, 46, 45  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
39instantiation74, 46, 47  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
41instantiation58, 48, 54  ⊢  
  : , :
42instantiation49, 50, 76, 51, 52, 53, 59, 60, 54  ⊢  
  : , : , : , : , : , :
43instantiation74, 68, 55  ⊢  
  : , : , :
44assumption  ⊢  
45instantiation74, 57, 56  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
47instantiation74, 57, 67  ⊢  
  : , : , :
48instantiation58, 59, 60  ⊢  
  : , :
49theorem  ⊢  
 proveit.numbers.multiplication.disassociation
50axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
52theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
53instantiation61  ⊢  
  : , :
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
55instantiation74, 72, 62  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
58theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
59instantiation74, 64, 63  ⊢  
  : , : , :
60instantiation74, 64, 65  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
62instantiation74, 66, 67  ⊢  
  : , : , :
63instantiation74, 68, 69  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
65instantiation74, 70, 71  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
67theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
68theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
69instantiation74, 72, 73  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
71theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
72theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
73instantiation74, 75, 76  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
76theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements