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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.exponentiation.product_of_posnat_powers
2reference6  ⊢  
3reference70  ⊢  
4instantiation46, 6  ⊢  
  :
5theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
6instantiation17, 7, 8, 9  ⊢  
  : , :
7instantiation73, 54, 10  ⊢  
  : , : , :
8instantiation11, 47, 12  ⊢  
  : , :
9instantiation13, 14, 15  ⊢  
  : , : , :
10instantiation73, 62, 16  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
12instantiation17, 37, 47, 25  ⊢  
  : , :
13theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
14instantiation18, 53, 19  ⊢  
  : , :
15instantiation34, 20  ⊢  
  : , : , :
16instantiation73, 68, 21  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.division.div_complex_closure
18theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
19instantiation73, 22, 23  ⊢  
  : , : , :
20instantiation24, 37, 47, 25, 26*  ⊢  
  : , :
21instantiation73, 74, 27  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
23instantiation28, 59, 29  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.division.div_as_mult
25instantiation30, 72  ⊢  
  :
26instantiation31, 32, 33  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
28theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
29instantiation73, 71, 50  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
31axiom  ⊢  
 proveit.logic.equality.equals_transitivity
32instantiation34, 35  ⊢  
  : , : , :
33instantiation36, 37, 38  ⊢  
  : , :
34axiom  ⊢  
 proveit.logic.equality.substitution
35instantiation39, 40, 70, 41*  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.multiplication.commutation
37instantiation73, 54, 42  ⊢  
  : , : , :
38instantiation73, 54, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
40instantiation73, 44, 45  ⊢  
  : , : , :
41instantiation46, 47  ⊢  
  :
42instantiation48, 49, 50  ⊢  
  : , : , :
43instantiation73, 62, 51  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
45instantiation73, 52, 53  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
47instantiation73, 54, 55  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
49instantiation56, 57  ⊢  
  : , :
50axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
51instantiation73, 58, 59  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
53instantiation73, 60, 61  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
55instantiation73, 62, 63  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
58theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
59instantiation64, 65, 66  ⊢  
  : , :
60theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
61instantiation73, 67, 72  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
63instantiation73, 68, 69  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
65instantiation73, 71, 70  ⊢  
  : , : , :
66instantiation73, 71, 72  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
68theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
69instantiation73, 74, 75  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
71theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
72theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
73theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
75theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements