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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.addition.subtraction.pos_difference
2instantiation3, 4, 5,  ⊢  
  : , : , :
3axiom  ⊢  
 proveit.numbers.ordering.transitivity_less_less
4instantiation6, 11, 33, 7  ⊢  
  : , : , :
5instantiation18, 8, 9,  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
7theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
8instantiation10, 33, 11, 12, 13, 14*  ⊢  
  : , : , :
9instantiation25, 15, 39, 16,  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
11theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
12instantiation48, 36, 17  ⊢  
  : , : , :
13instantiation18, 19, 20  ⊢  
  : , : , :
14instantiation21, 22, 23  ⊢  
  : , : , :
15instantiation38, 24, 42  ⊢  
  : , :
16assumption  ⊢  
17instantiation48, 41, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
19theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
20instantiation25, 42, 35, 31  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
22instantiation26, 28  ⊢  
  :
23instantiation27, 28, 29  ⊢  
  : , :
24instantiation48, 30, 31  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
26theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
27theorem  ⊢  
 proveit.numbers.addition.commutation
28instantiation48, 32, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
30instantiation34, 42, 35  ⊢  
  : , :
31assumption  ⊢  
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation48, 36, 37  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
35instantiation38, 39, 40  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
37instantiation48, 41, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
39instantiation48, 43, 44  ⊢  
  : , : , :
40instantiation45, 46  ⊢  
  :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation48, 49, 47  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
44theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
45theorem  ⊢  
 proveit.numbers.negation.int_closure
46instantiation48, 49, 50  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
48theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements