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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,  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
2instantiation3, 4, 61,  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
4instantiation5, 6, 7,  ⊢  
  :
5theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
6instantiation49, 8, 9,  ⊢  
  : , :
7instantiation10, 11,  ⊢  
  : , :
8instantiation59, 12, 27,  ⊢  
  : , : , :
9instantiation59, 13, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.ordering.relax_less
11instantiation15, 16,  ⊢  
  : , :
12instantiation45, 26, 50  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
14instantiation17, 18  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
16instantiation29, 19, 20,  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
18theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
19instantiation21, 44, 22, 23, 24, 25*  ⊢  
  : , : , :
20instantiation36, 26, 50, 27,  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
23instantiation59, 47, 28  ⊢  
  : , : , :
24instantiation29, 30, 31  ⊢  
  : , : , :
25instantiation32, 33, 34  ⊢  
  : , : , :
26instantiation49, 35, 53  ⊢  
  : , :
27assumption  ⊢  
28instantiation59, 52, 35  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
30theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
31instantiation36, 53, 46, 42  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
33instantiation37, 39  ⊢  
  :
34instantiation38, 39, 40  ⊢  
  : , :
35instantiation59, 41, 42  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
37theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
38theorem  ⊢  
 proveit.numbers.addition.commutation
39instantiation59, 43, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
41instantiation45, 53, 46  ⊢  
  : , :
42assumption  ⊢  
43theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
44instantiation59, 47, 48  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
46instantiation49, 50, 51  ⊢  
  : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
48instantiation59, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
50instantiation59, 54, 55  ⊢  
  : , : , :
51instantiation56, 57  ⊢  
  :
52theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
53instantiation59, 60, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
55theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
56theorem  ⊢  
 proveit.numbers.negation.int_closure
57instantiation59, 60, 61  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
59theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
61theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements