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  ⊢  
  : , : , :
1reference45  ⊢  
2reference41  ⊢  
3instantiation45, 43, 4  ⊢  
  : , : , :
4instantiation45, 5, 6  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
6instantiation7, 19, 8, 9, 10  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
8instantiation12, 19, 11  ⊢  
  :
9instantiation12, 47, 13  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
11instantiation16, 14, 15  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.n_in_digits
13instantiation16, 17, 18  ⊢  
  : , :
14instantiation29, 19  ⊢  
  :
15instantiation20, 21  ⊢  
  :
16theorem  ⊢  
 proveit.logic.booleans.conjunction.and_if_both
17instantiation29, 47  ⊢  
  :
18instantiation22, 40, 23, 24, 25, 26*, 27*  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
20theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
21theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat9
22theorem  ⊢  
 proveit.numbers.addition.weak_bound_via_left_term_bound
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
24instantiation45, 41, 28  ⊢  
  : , : , :
25instantiation29, 38  ⊢  
  :
26instantiation30, 31, 32  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.add_4_5
28instantiation45, 43, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_lower_bound
30theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
31instantiation34, 36  ⊢  
  :
32instantiation35, 36, 37  ⊢  
  : , :
33instantiation45, 46, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
35theorem  ⊢  
 proveit.numbers.addition.commutation
36instantiation45, 39, 40  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
40instantiation45, 41, 42  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation45, 43, 44  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation45, 46, 47  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
*equality replacement requirements