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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, 3, 4, 5*  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_as_mult
2reference33  ⊢  
3instantiation6, 27  ⊢  
  :
4instantiation7, 14, 8  ⊢  
  : , :
5instantiation9, 10, 11  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.sqrt_complex_closure
7theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
8instantiation12, 13, 14  ⊢  
  : , :
9axiom  ⊢  
 proveit.logic.equality.equals_transitivity
10instantiation15, 16  ⊢  
  : , : , :
11instantiation17, 18  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.division.div_rational_nonzero_closure
13instantiation61, 20, 19  ⊢  
  : , : , :
14instantiation61, 20, 21  ⊢  
  : , : , :
15axiom  ⊢  
 proveit.logic.equality.substitution
16instantiation22, 27, 46, 23, 24, 25*  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
18instantiation26, 27, 28  ⊢  
  : , :
19instantiation61, 29, 60  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
21instantiation61, 29, 63  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
23instantiation61, 50, 30  ⊢  
  : , : , :
24instantiation31, 63  ⊢  
  :
25instantiation32, 40, 33, 34*  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
27instantiation61, 45, 35  ⊢  
  : , : , :
28instantiation61, 45, 36  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
30instantiation61, 48, 37  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
32theorem  ⊢  
 proveit.numbers.negation.pos_times_neg
33instantiation61, 45, 38  ⊢  
  : , : , :
34instantiation39, 40  ⊢  
  :
35instantiation61, 50, 41  ⊢  
  : , : , :
36instantiation42, 46  ⊢  
  :
37instantiation43, 49  ⊢  
  :
38instantiation61, 50, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
40instantiation61, 45, 46  ⊢  
  : , : , :
41instantiation61, 48, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.negation.real_closure
43theorem  ⊢  
 proveit.numbers.negation.int_closure
44instantiation61, 48, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
46instantiation61, 50, 51  ⊢  
  : , : , :
47instantiation61, 53, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
49instantiation61, 53, 54  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation61, 55, 56  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
56instantiation57, 58, 59  ⊢  
  : , :
57theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
58instantiation61, 62, 60  ⊢  
  : , : , :
59instantiation61, 62, 63  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
61theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
63theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements