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	51	⊢
3	reference	48	⊢
4	reference	9	⊢
5	instantiation	7	⊢
	: , :
6	instantiation	8, 51, 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	14, 15	⊢
	: , :
11	instantiation	19, 48, 51, 16	⊢
	: , :
12	instantiation	19, 48, 17, 18	⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
14	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
15	instantiation	19, 20, 48, 21	⊢
	: , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
18	instantiation	22, 39, 23, 41, 24, 25^, 26^	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
21	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
22	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
24	instantiation	27, 28	⊢
	:
25	instantiation	31, 29, 30	⊢
	: , : , :
26	instantiation	31, 32, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
29	instantiation	34, 37	⊢
	:
30	instantiation	36, 37, 35	⊢
	: , :
31	theorem		⊢
	proveit.logic.equality.sub_right_side_into
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
33	instantiation	36, 37, 38	⊢
	: , :
34	theorem		⊢
	proveit.numbers.addition.elim_zero_right
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
36	theorem		⊢
	proveit.numbers.addition.commutation
37	instantiation	49, 40, 39	⊢
	: , : , :
38	instantiation	49, 40, 41	⊢
	: , : , :
39	instantiation	49, 43, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	49, 43, 44	⊢
	: , : , :
42	instantiation	49, 46, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	49, 46, 47	⊢
	: , : , :
45	instantiation	49, 50, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	49, 50, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements