Show the Proof

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

	step type	requirements	statement
0	instantiation	1, 2*	⊢
	: , :
1	axiom		⊢
	proveit.logic.equality.not_equals_def
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 7	⊢
	: , : , :
5	axiom		⊢
	proveit.logic.booleans.negation.not_f
6	axiom		⊢
	proveit.logic.equality.substitution
7	instantiation	8, 9	⊢
	:
8	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
9	instantiation	10, 11	⊢
	: , :
10	theorem		⊢
	proveit.logic.equality.unfold_not_equals
11	instantiation	12, 13	⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
13	instantiation	14, 39, 15, 16	⊢
	: , :
14	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
16	instantiation	17, 32, 18, 19, 20*, 21*	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
19	instantiation	22, 23	⊢
	:
20	instantiation	24, 25, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
24	theorem		⊢
	proveit.logic.equality.sub_right_side_into
25	instantiation	27, 29	⊢
	:
26	instantiation	28, 29, 30	⊢
	: , :
27	theorem		⊢
	proveit.numbers.addition.elim_zero_right
28	theorem		⊢
	proveit.numbers.addition.commutation
29	instantiation	37, 31, 32	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	37, 33, 34	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	37, 35, 36	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
36	instantiation	37, 38, 39	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements