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	⊢
	: , : , :
1	reference	5	⊢
2	instantiation	24, 3, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	: , : , :
4	instantiation	7, 50, 63, 8^*	⊢
	: , : , : , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	9, 21, 20, 10^, 11^	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
8	instantiation	24, 12, 13	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.division.prod_of_fracs
10	instantiation	45, 21	⊢
	:
11	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
12	instantiation	32, 33, 14, 15, 16, 17	⊢
	: , : , : , :
13	instantiation	18, 19, 20, 21, 22^, 23^	⊢
	: , : , :
14	instantiation	43	⊢
	: , :
15	instantiation	43	⊢
	: , :
16	instantiation	24, 25, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
18	theorem		⊢
	proveit.numbers.division.frac_cancel_left
19	instantiation	64, 28, 27	⊢
	: , : , :
20	instantiation	64, 28, 29	⊢
	: , : , :
21	instantiation	64, 52, 30	⊢
	: , : , :
22	instantiation	45, 31	⊢
	:
23	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	32, 33, 34, 35, 36, 37	⊢
	: , : , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
27	instantiation	64, 39, 38	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
29	instantiation	64, 39, 40	⊢
	: , : , :
30	instantiation	64, 59, 41	⊢
	: , : , :
31	instantiation	64, 52, 42	⊢
	: , : , :
32	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
34	instantiation	43	⊢
	: , :
35	instantiation	43	⊢
	: , :
36	instantiation	44, 46	⊢
	:
37	instantiation	45, 46	⊢
	:
38	instantiation	64, 48, 47	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
40	instantiation	64, 48, 49	⊢
	: , : , :
41	instantiation	64, 62, 50	⊢
	: , : , :
42	instantiation	64, 59, 51	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
45	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
46	instantiation	64, 52, 53	⊢
	: , : , :
47	instantiation	64, 55, 54	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
49	instantiation	64, 55, 56	⊢
	: , : , :
50	instantiation	64, 65, 57	⊢
	: , : , :
51	instantiation	64, 62, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	instantiation	64, 59, 60	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
58	instantiation	64, 65, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	64, 62, 63	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
63	instantiation	64, 65, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements