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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 43, 7, 23, 8*, 9*  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation10, 43, 18, 19  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.posnat_power_of_product
7instantiation11, 18, 12  ⊢  
  : , :
8instantiation13, 14, 15, 16  ⊢  
  : , : , : , :
9instantiation17, 18, 21, 47, 19, 20*  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.division.div_as_mult
11theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
12instantiation55, 46, 21  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
14instantiation22, 23, 43  ⊢  
  : , :
15instantiation24, 57, 25, 26, 27  ⊢  
  : , : , : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
17theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
18instantiation55, 46, 28  ⊢  
  : , : , :
19instantiation29, 30  ⊢  
  :
20instantiation31, 32, 43, 33*  ⊢  
  : , :
21instantiation55, 50, 34  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.exp_nat_pos_expansion
23theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
24theorem  ⊢  
 proveit.core_expr_types.operations.operands_substitution_via_tuple
25instantiation35, 57  ⊢  
  : , :
26instantiation36  ⊢  
  : , :
27instantiation37  ⊢  
  :
28instantiation55, 38, 40  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
30instantiation55, 39, 40  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_left
32instantiation55, 46, 41  ⊢  
  : , : , :
33instantiation42, 43  ⊢  
  :
34instantiation55, 53, 44  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.core_expr_types.tuples.range_from1_len_typical_eq
36theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37theorem  ⊢  
 proveit.numbers.numerals.decimals.reduce_2_repeats
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
41instantiation55, 50, 45  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
43instantiation55, 46, 47  ⊢  
  : , : , :
44instantiation48, 49  ⊢  
  :
45instantiation55, 53, 49  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation55, 50, 51  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.negation.int_closure
49instantiation55, 56, 52  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation55, 53, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
53theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
54instantiation55, 56, 57  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements