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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  ⊢  
  : , : , : , :
1reference34  ⊢  
2instantiation31, 5, 6, 7, 8*  ⊢  
  : , :
3instantiation9  ⊢  
  :
4instantiation10, 11  ⊢  
  : , :
5instantiation77, 68, 12  ⊢  
  : , : , :
6instantiation77, 68, 13  ⊢  
  : , : , :
7instantiation14, 39, 65, 40  ⊢  
  : , :
8instantiation38, 39, 69, 43, 40, 15*  ⊢  
  : , : , :
9axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
10theorem  ⊢  
 proveit.logic.equality.equals_reversal
11instantiation16, 17, 18  ⊢  
  : , : , :
12instantiation77, 72, 19  ⊢  
  : , : , :
13instantiation20, 50, 79  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.exp_not_eq_zero
15instantiation21, 65, 54, 22*  ⊢  
  : , :
16axiom  ⊢  
 proveit.logic.equality.equals_transitivity
17instantiation23, 24  ⊢  
  : , : , :
18instantiation25, 65, 26, 45, 27*, 28*  ⊢  
  : , : , :
19instantiation77, 75, 29  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
21theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
22instantiation30, 65  ⊢  
  :
23axiom  ⊢  
 proveit.logic.equality.substitution
24instantiation31, 65, 39, 40  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.exponentiation.posnat_power_of_product
26instantiation32, 39, 33  ⊢  
  : , :
27instantiation34, 35, 36, 37  ⊢  
  : , : , : , :
28instantiation38, 39, 43, 69, 40, 41*  ⊢  
  : , : , :
29instantiation77, 78, 42  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
31theorem  ⊢  
 proveit.numbers.division.div_as_mult
32theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
33instantiation77, 68, 43  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
35instantiation44, 45, 65  ⊢  
  : , :
36instantiation46, 79, 47, 48, 49  ⊢  
  : , : , : , :
37theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
38theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
39instantiation77, 68, 50  ⊢  
  : , : , :
40instantiation51, 52  ⊢  
  :
41instantiation53, 54, 65, 55*  ⊢  
  : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
43instantiation77, 72, 56  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.exponentiation.exp_nat_pos_expansion
45theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
46theorem  ⊢  
 proveit.core_expr_types.operations.operands_substitution_via_tuple
47instantiation57, 79  ⊢  
  : , :
48instantiation58  ⊢  
  : , :
49instantiation59  ⊢  
  :
50instantiation77, 60, 62  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
52instantiation77, 61, 62  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_left
54instantiation77, 68, 63  ⊢  
  : , : , :
55instantiation64, 65  ⊢  
  :
56instantiation77, 75, 66  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.core_expr_types.tuples.range_from1_len_typical_eq
58theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
59theorem  ⊢  
 proveit.numbers.numerals.decimals.reduce_2_repeats
60theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
62theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
63instantiation77, 72, 67  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
65instantiation77, 68, 69  ⊢  
  : , : , :
66instantiation70, 71  ⊢  
  :
67instantiation77, 75, 71  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
69instantiation77, 72, 73  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.negation.int_closure
71instantiation77, 78, 74  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
73instantiation77, 75, 76  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
75theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
76instantiation77, 78, 79  ⊢  
  : , : , :
77theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
78theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
79theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements