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	24	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 65, 63, 8^*	⊢
	: , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	46, 9	⊢
	:
6	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
7	instantiation	67, 68, 10	⊢
	: , : , :
8	instantiation	24, 11, 12	⊢
	: , : , :
9	instantiation	67, 55, 13	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
11	instantiation	32, 66, 14, 15, 16, 17	⊢
	: , : , : , :
12	instantiation	18, 19, 20, 45, 21^, 22^	⊢
	: , : , :
13	instantiation	67, 61, 23	⊢
	: , : , :
14	instantiation	43	⊢
	: , :
15	instantiation	43	⊢
	: , :
16	instantiation	24, 25, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_2
18	theorem		⊢
	proveit.numbers.division.frac_cancel_left
19	instantiation	67, 28, 27	⊢
	: , : , :
20	instantiation	67, 28, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
22	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_3
23	instantiation	67, 30, 31	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	32, 66, 33, 34, 35, 36	⊢
	: , : , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_6
27	instantiation	67, 38, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
29	instantiation	67, 38, 39	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
31	instantiation	40, 41, 42	⊢
	: , :
32	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
33	instantiation	43	⊢
	: , :
34	instantiation	43	⊢
	: , :
35	instantiation	44, 45	⊢
	:
36	instantiation	46, 47	⊢
	:
37	instantiation	67, 49, 48	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
39	instantiation	67, 49, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
41	instantiation	67, 52, 51	⊢
	: , : , :
42	instantiation	67, 52, 53	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
45	instantiation	67, 55, 54	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
47	instantiation	67, 55, 56	⊢
	: , : , :
48	instantiation	67, 58, 57	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
50	instantiation	67, 58, 59	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
54	instantiation	67, 61, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	67, 61, 62	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
60	instantiation	67, 64, 63	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
62	instantiation	67, 64, 65	⊢
	: , : , :
63	instantiation	67, 68, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	67, 68, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
^*equality replacement requirements