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 type	requirements	statement
0	instantiation	1, 2, 3, 4, 5	⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
2	reference	46	⊢
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
4	reference	7	⊢
5	instantiation	6, 46, 7, 8, 9, 10	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
7	instantiation	11	⊢
	: , : , :
8	instantiation	12, 13	⊢
	: , :
9	instantiation	18, 46, 14, 15	⊢
	: , :
10	instantiation	18, 46, 16, 17	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
12	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
13	instantiation	18, 37, 46, 19	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
15	instantiation	20, 39, 21, 22, 23, 24^, 25^	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
17	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
18	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
19	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
20	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
22	instantiation	44, 40, 26	⊢
	: , : , :
23	instantiation	27, 28	⊢
	:
24	instantiation	29, 30, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
26	instantiation	44, 42, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
29	theorem		⊢
	proveit.logic.equality.sub_right_side_into
30	instantiation	33, 35	⊢
	:
31	instantiation	34, 35, 36	⊢
	: , :
32	instantiation	44, 45, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.elim_zero_right
34	theorem		⊢
	proveit.numbers.addition.commutation
35	instantiation	44, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	44, 40, 41	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	44, 42, 43	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	44, 45, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements