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,  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
2instantiation68, 3, 4,  ⊢  
  : , : , :
3theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
4instantiation5, 10, 6,  ⊢  
  :
5theorem  ⊢  
 proveit.numbers.exponentiation.sqrd_pos_closure
6instantiation7, 8,  ⊢  
  : , :
7theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
8instantiation9, 31, 10, 11,  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq
10instantiation12, 13, 14,  ⊢  
  : , :
11instantiation15, 16,  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
13instantiation68, 56, 17,  ⊢  
  : , : , :
14instantiation18, 19  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
16instantiation20, 21, 22,  ⊢  
  : , : , :
17instantiation68, 61, 23,  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.negation.real_closure
19instantiation24, 31, 53, 26  ⊢  
  : , : , :
20axiom  ⊢  
 proveit.numbers.ordering.transitivity_less_less
21instantiation25, 31, 53, 26  ⊢  
  : , : , :
22instantiation38, 27, 28,  ⊢  
  : , : , :
23instantiation68, 29, 35,  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
26theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
27instantiation30, 53, 31, 32, 33, 34*  ⊢  
  : , : , :
28instantiation45, 36, 59, 35,  ⊢  
  : , : , :
29instantiation54, 36, 59  ⊢  
  : , :
30theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
32instantiation68, 56, 37  ⊢  
  : , : , :
33instantiation38, 39, 40  ⊢  
  : , : , :
34instantiation41, 42, 43  ⊢  
  : , : , :
35assumption  ⊢  
36instantiation58, 44, 62  ⊢  
  : , :
37instantiation68, 61, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
39theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
40instantiation45, 62, 55, 51  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
42instantiation46, 48  ⊢  
  :
43instantiation47, 48, 49  ⊢  
  : , :
44instantiation68, 50, 51  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
46theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
47theorem  ⊢  
 proveit.numbers.addition.commutation
48instantiation68, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
50instantiation54, 62, 55  ⊢  
  : , :
51assumption  ⊢  
52theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
53instantiation68, 56, 57  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
55instantiation58, 59, 60  ⊢  
  : , :
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
57instantiation68, 61, 62  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
59instantiation68, 63, 64  ⊢  
  : , : , :
60instantiation65, 66  ⊢  
  :
61theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
62instantiation68, 69, 67  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
64theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
65theorem  ⊢  
 proveit.numbers.negation.int_closure
66instantiation68, 69, 70  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
68theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
70theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements