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, 6	⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
2	reference	53	⊢
3	reference	50	⊢
4	reference	9	⊢
5	instantiation	7	⊢
	: , :
6	instantiation	8, 53, 9, 10, 11, 12	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
8	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
9	instantiation	13	⊢
	: , : , :
10	instantiation	15, 14	⊢
	: , :
11	instantiation	15, 16	⊢
	: , :
12	instantiation	20, 22, 17, 18	⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
14	instantiation	20, 50, 22, 19	⊢
	: , :
15	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
16	instantiation	20, 21, 22, 23	⊢
	: , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
18	theorem		⊢
	proveit.numbers.numerals.decimals.less_5_6
19	instantiation	24, 41, 25, 43, 26, 27^, 28^	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
23	theorem		⊢
	proveit.numbers.numerals.decimals.less_4_5
24	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
26	instantiation	29, 30	⊢
	:
27	instantiation	33, 31, 32	⊢
	: , : , :
28	instantiation	33, 34, 35	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
31	instantiation	36, 39	⊢
	:
32	instantiation	38, 39, 37	⊢
	: , :
33	theorem		⊢
	proveit.logic.equality.sub_right_side_into
34	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
35	instantiation	38, 39, 40	⊢
	: , :
36	theorem		⊢
	proveit.numbers.addition.elim_zero_right
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
38	theorem		⊢
	proveit.numbers.addition.commutation
39	instantiation	51, 42, 41	⊢
	: , : , :
40	instantiation	51, 42, 43	⊢
	: , : , :
41	instantiation	51, 45, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	instantiation	51, 45, 46	⊢
	: , : , :
44	instantiation	51, 48, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	51, 48, 49	⊢
	: , : , :
47	instantiation	51, 52, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	51, 52, 53	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements