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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.inclusion.refined_nonmembership
2	instantiation	4, 19, 47, 5	⊢
	: , : , : , :
3	instantiation	6, 50, 7, 8, 9, 10	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.subset_eq_of_superset
5	instantiation	11	⊢
	: , :
6	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
7	instantiation	12	⊢
	: , : , :
8	instantiation	13, 14	⊢
	: , :
9	instantiation	18, 47, 50, 15	⊢
	: , :
10	instantiation	18, 47, 16, 17	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
13	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
14	instantiation	18, 19, 47, 20	⊢
	: , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
17	instantiation	21, 38, 22, 40, 23, 24^, 25^	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
20	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
21	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
23	instantiation	26, 27	⊢
	:
24	instantiation	30, 28, 29	⊢
	: , : , :
25	instantiation	30, 31, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
28	instantiation	33, 36	⊢
	:
29	instantiation	35, 36, 34	⊢
	: , :
30	theorem		⊢
	proveit.logic.equality.sub_right_side_into
31	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
32	instantiation	35, 36, 37	⊢
	: , :
33	theorem		⊢
	proveit.numbers.addition.elim_zero_right
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
35	theorem		⊢
	proveit.numbers.addition.commutation
36	instantiation	48, 39, 38	⊢
	: , : , :
37	instantiation	48, 39, 40	⊢
	: , : , :
38	instantiation	48, 42, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	48, 42, 43	⊢
	: , : , :
41	instantiation	48, 45, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	48, 45, 46	⊢
	: , : , :
44	instantiation	48, 49, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	48, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements