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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.multiplication.mult_not_eq_zero
2reference38  ⊢  
3instantiation6  ⊢  
  : , :
4instantiation9, 7, 8  ⊢  
  :
5instantiation9, 10, 11  ⊢  
  :
6theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
7instantiation12, 15  ⊢  
  :
8instantiation17, 21, 13  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
10instantiation14, 15, 16  ⊢  
  : , :
11instantiation17, 21, 18  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.sqrt_complex_closure
13instantiation19, 20, 21  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
15instantiation47, 23, 22  ⊢  
  : , : , :
16instantiation47, 23, 24  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
18instantiation47, 25, 36  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.division.div_rational_nonzero_closure
20instantiation47, 27, 26  ⊢  
  : , : , :
21instantiation47, 27, 28  ⊢  
  : , : , :
22instantiation47, 30, 29  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
24instantiation47, 30, 31  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
26instantiation47, 32, 46  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
28instantiation47, 32, 49  ⊢  
  : , : , :
29instantiation47, 33, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
31instantiation47, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
34instantiation47, 37, 38  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
36instantiation39, 40, 41  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
39theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
40instantiation42, 43, 44  ⊢  
  : , :
41instantiation47, 48, 45  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
43instantiation47, 48, 46  ⊢  
  : , : , :
44instantiation47, 48, 49  ⊢  
  : , : , :
45assumption  ⊢  
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2