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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, 6, 7, 8, 9  ⊢  
  : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.addition.disassociation
2theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
3reference45  ⊢  
4axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
5instantiation10  ⊢  
  : , :
6theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7instantiation43, 12, 14  ⊢  
  : , : , :
8instantiation43, 12, 11  ⊢  
  : , : , :
9instantiation43, 12, 13  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11instantiation22, 14  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
13instantiation15, 16, 27  ⊢  
  : , :
14instantiation17, 18, 19, 20  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
16instantiation43, 35, 21  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
18instantiation22, 23  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
20assumption  ⊢  
21instantiation43, 24, 25  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.negation.real_closure
23instantiation26, 27, 28, 29  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
25instantiation30, 31, 32  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.division.div_real_closure
27instantiation43, 33, 34  ⊢  
  : , : , :
28instantiation43, 35, 36  ⊢  
  : , : , :
29instantiation37, 40  ⊢  
  :
30theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
31instantiation43, 39, 38  ⊢  
  : , : , :
32instantiation43, 39, 40  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
36instantiation43, 41, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
38theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
40theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation43, 44, 45  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2