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	27	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 69, 8, 9^*	⊢
	: , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	33, 10	⊢
	:
6	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
7	instantiation	70, 71, 11	⊢
	: , : , :
8	instantiation	70, 71, 12	⊢
	: , : , :
9	instantiation	27, 13, 14	⊢
	: , : , :
10	instantiation	70, 59, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
13	instantiation	38, 72, 16, 17, 18, 19	⊢
	: , : , : , :
14	instantiation	20, 21, 22, 52, 23^, 24^, 25^*	⊢
	: , : , :
15	instantiation	70, 65, 26	⊢
	: , : , :
16	instantiation	50	⊢
	: , :
17	instantiation	50	⊢
	: , :
18	instantiation	27, 28, 29	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
20	theorem		⊢
	proveit.numbers.division.frac_cancel_left
21	instantiation	70, 31, 30	⊢
	: , : , :
22	instantiation	70, 31, 32	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
24	instantiation	33, 34	⊢
	:
25	instantiation	35, 52	⊢
	:
26	instantiation	70, 36, 37	⊢
	: , : , :
27	axiom		⊢
	proveit.logic.equality.equals_transitivity
28	instantiation	38, 72, 39, 40, 41, 42	⊢
	: , : , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_6
30	instantiation	70, 44, 43	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
32	instantiation	70, 44, 45	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
34	instantiation	70, 59, 46	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.frac_one_denom
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
37	instantiation	47, 48, 49	⊢
	: , :
38	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
39	instantiation	50	⊢
	: , :
40	instantiation	50	⊢
	: , :
41	instantiation	51, 52	⊢
	:
42	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_3
43	instantiation	70, 54, 53	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
45	instantiation	70, 54, 55	⊢
	: , : , :
46	instantiation	70, 65, 56	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
48	instantiation	70, 57, 63	⊢
	: , : , :
49	instantiation	70, 57, 58	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
51	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
52	instantiation	70, 59, 60	⊢
	: , : , :
53	instantiation	70, 62, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
55	instantiation	70, 62, 63	⊢
	: , : , :
56	instantiation	70, 68, 64	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
60	instantiation	70, 65, 66	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
64	instantiation	70, 71, 67	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
66	instantiation	70, 68, 69	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
69	instantiation	70, 71, 72	⊢
	: , : , :
70	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements