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,  ⊢  
  : , : , :
1reference62  ⊢  
2theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
3instantiation62, 4, 5,  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
5instantiation6, 7, 64,  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
7instantiation8, 9, 10,  ⊢  
  :
8theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
9instantiation52, 11, 12,  ⊢  
  : , :
10instantiation13, 14,  ⊢  
  : , :
11instantiation62, 15, 30,  ⊢  
  : , : , :
12instantiation62, 16, 17  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.ordering.relax_less
14instantiation18, 19,  ⊢  
  : , :
15instantiation48, 29, 53  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
17instantiation20, 21  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
19instantiation32, 22, 23,  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
21theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
22instantiation24, 47, 25, 26, 27, 28*  ⊢  
  : , : , :
23instantiation39, 29, 53, 30,  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
26instantiation62, 50, 31  ⊢  
  : , : , :
27instantiation32, 33, 34  ⊢  
  : , : , :
28instantiation35, 36, 37  ⊢  
  : , : , :
29instantiation52, 38, 56  ⊢  
  : , :
30assumption  ⊢  
31instantiation62, 55, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
33theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
34instantiation39, 56, 49, 45  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
36instantiation40, 42  ⊢  
  :
37instantiation41, 42, 43  ⊢  
  : , :
38instantiation62, 44, 45  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
40theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
41theorem  ⊢  
 proveit.numbers.addition.commutation
42instantiation62, 46, 47  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
44instantiation48, 56, 49  ⊢  
  : , :
45assumption  ⊢  
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation62, 50, 51  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
49instantiation52, 53, 54  ⊢  
  : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation62, 55, 56  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
53instantiation62, 57, 58  ⊢  
  : , : , :
54instantiation59, 60  ⊢  
  :
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
56instantiation62, 63, 61  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
58theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
59theorem  ⊢  
 proveit.numbers.negation.int_closure
60instantiation62, 63, 64  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
62theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
64theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements