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,  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
2instantiation4, 10, 11, 12,  ⊢  
  : , : , :
3instantiation21, 5, 6,  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
5instantiation7, 8  ⊢  
  : , :
6instantiation9, 10, 11, 12,  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
8instantiation13, 37, 14, 15, 16, 17*  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound
10instantiation59, 41, 18  ⊢  
  : , : , :
11instantiation59, 41, 19  ⊢  
  : , : , :
12assumption  ⊢  
13theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
14theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
15instantiation59, 41, 20  ⊢  
  : , : , :
16instantiation21, 22, 23  ⊢  
  : , : , :
17instantiation24, 25, 26  ⊢  
  : , : , :
18instantiation59, 47, 27  ⊢  
  : , : , :
19instantiation59, 47, 28  ⊢  
  : , : , :
20instantiation59, 47, 38  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
22theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
23instantiation29, 49, 50, 44  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
25instantiation30, 32  ⊢  
  :
26instantiation31, 32, 33  ⊢  
  : , :
27instantiation52, 34, 35  ⊢  
  : , :
28instantiation52, 53, 35  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
30theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
31theorem  ⊢  
 proveit.numbers.addition.commutation
32instantiation59, 36, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
34instantiation52, 38, 49  ⊢  
  : , :
35instantiation59, 39, 40  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
37instantiation59, 41, 42  ⊢  
  : , : , :
38instantiation59, 43, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
40instantiation45, 46  ⊢  
  :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation59, 47, 49  ⊢  
  : , : , :
43instantiation48, 49, 50  ⊢  
  : , :
44assumption  ⊢  
45theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
49instantiation59, 60, 51  ⊢  
  : , : , :
50instantiation52, 53, 54  ⊢  
  : , :
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
52theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
53instantiation59, 55, 56  ⊢  
  : , : , :
54instantiation57, 58  ⊢  
  :
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
56theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
57theorem  ⊢  
 proveit.numbers.negation.int_closure
58instantiation59, 60, 61  ⊢  
  : , : , :
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