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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  ⊢  
  : , : , :
1reference8  ⊢  
2instantiation3, 11, 24, 20, 4*  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_as_mult
4instantiation5, 6, 7  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation8, 9  ⊢  
  : , : , :
7instantiation10, 11, 12  ⊢  
  : , :
8axiom  ⊢  
 proveit.logic.equality.substitution
9instantiation13, 14, 15, 16*  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.multiplication.commutation
11instantiation44, 31, 17  ⊢  
  : , : , :
12instantiation18, 19, 24, 20  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
14instantiation44, 21, 22  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
16instantiation23, 24  ⊢  
  :
17instantiation44, 25, 26  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.division.div_complex_closure
19instantiation44, 31, 27  ⊢  
  : , : , :
20instantiation28, 40  ⊢  
  :
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22instantiation44, 29, 30  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
24instantiation44, 31, 32  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
26assumption  ⊢  
27instantiation44, 36, 33  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30instantiation44, 34, 35  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
32instantiation44, 36, 37  ⊢  
  : , : , :
33instantiation44, 41, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
35instantiation44, 39, 40  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
37instantiation44, 41, 42  ⊢  
  : , : , :
38instantiation44, 45, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
40theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation44, 45, 46  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
44theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements