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	reference	41	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	9, 50, 10, 11, 12, 13	⊢
	: , : , :
6	assumption		⊢
7	axiom		⊢
	proveit.logic.equality.substitution
8	instantiation	14, 15	⊢
	: , :
9	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
10	instantiation	16	⊢
	: , : , :
11	instantiation	19, 17	⊢
	: , :
12	instantiation	19, 18	⊢
	: , :
13	instantiation	19, 20	⊢
	: , :
14	theorem		⊢
	proveit.logic.equality.equals_reversal
15	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
17	instantiation	23, 60, 24, 21	⊢
	: , :
18	instantiation	23, 63, 24, 22	⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
20	instantiation	23, 50, 24, 25	⊢
	: , :
21	instantiation	30, 51, 31, 26, 27, 28^, 29^	⊢
	: , : , :
22	instantiation	30, 53, 31, 32, 33^, 34^	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
25	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
26	instantiation	61, 55, 35	⊢
	: , : , :
27	instantiation	39, 36	⊢
	:
28	instantiation	41, 37, 38	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
30	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
32	instantiation	39, 40	⊢
	:
33	instantiation	41, 42, 43	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
35	instantiation	61, 58, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
37	instantiation	46, 45	⊢
	:
38	instantiation	47, 45, 49	⊢
	: , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.logic.equality.sub_right_side_into
42	instantiation	46, 48	⊢
	:
43	instantiation	47, 48, 49	⊢
	: , :
44	instantiation	61, 62, 50	⊢
	: , : , :
45	instantiation	61, 52, 51	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.elim_zero_right
47	theorem		⊢
	proveit.numbers.addition.commutation
48	instantiation	61, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
51	instantiation	61, 55, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	instantiation	61, 55, 56	⊢
	: , : , :
54	instantiation	61, 58, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	61, 58, 59	⊢
	: , : , :
57	instantiation	61, 62, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
59	instantiation	61, 62, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements