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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, 7  ⊢  
  :
4axiom  ⊢  
 proveit.logic.equality.substitution
5assumption  ⊢  
6axiom  ⊢  
 proveit.logic.booleans.negation.negation_elim
7instantiation8, 9  ⊢  
  : , :
8theorem  ⊢  
 proveit.logic.equality.unfold_not_equals
9instantiation10, 11  ⊢  
  : , :
10theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
11instantiation12, 41, 13, 14  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_nat
13theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
14instantiation15, 34, 16, 17, 18, 19*, 20*  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
16theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
17instantiation39, 35, 21  ⊢  
  : , : , :
18instantiation22, 23  ⊢  
  :
19instantiation24, 25, 26  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.add_3_1
21instantiation39, 37, 27  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
23theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
24theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
25instantiation28, 30  ⊢  
  :
26instantiation29, 30, 31  ⊢  
  : , :
27instantiation39, 40, 32  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
29theorem  ⊢  
 proveit.numbers.addition.commutation
30instantiation39, 33, 34  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
32theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
34instantiation39, 35, 36  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
36instantiation39, 37, 38  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
38instantiation39, 40, 41  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
41theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements