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	28, 3, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	: , : , :
4	instantiation	7, 8, 70, 9, 10^*	⊢
	: , : , : , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	34, 11	⊢
	:
7	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
8	instantiation	71, 72, 12	⊢
	: , : , :
9	instantiation	71, 72, 13	⊢
	: , : , :
10	instantiation	28, 14, 15	⊢
	: , : , :
11	instantiation	71, 60, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
14	instantiation	39, 73, 17, 18, 19, 20	⊢
	: , : , : , :
15	instantiation	21, 22, 23, 53, 24^, 25^, 26^*	⊢
	: , : , :
16	instantiation	71, 66, 27	⊢
	: , : , :
17	instantiation	51	⊢
	: , :
18	instantiation	51	⊢
	: , :
19	instantiation	28, 29, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
21	theorem		⊢
	proveit.numbers.division.frac_cancel_left
22	instantiation	71, 32, 31	⊢
	: , : , :
23	instantiation	71, 32, 33	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
25	instantiation	34, 35	⊢
	:
26	instantiation	36, 53	⊢
	:
27	instantiation	71, 37, 38	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	39, 73, 40, 41, 42, 43	⊢
	: , : , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_6
31	instantiation	71, 45, 44	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
33	instantiation	71, 45, 46	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
35	instantiation	71, 60, 47	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.division.frac_one_denom
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
38	instantiation	48, 49, 50	⊢
	: , :
39	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
40	instantiation	51	⊢
	: , :
41	instantiation	51	⊢
	: , :
42	instantiation	52, 53	⊢
	:
43	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_3
44	instantiation	71, 55, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
46	instantiation	71, 55, 56	⊢
	: , : , :
47	instantiation	71, 66, 57	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
49	instantiation	71, 58, 64	⊢
	: , : , :
50	instantiation	71, 58, 59	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
52	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
53	instantiation	71, 60, 61	⊢
	: , : , :
54	instantiation	71, 63, 62	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
56	instantiation	71, 63, 64	⊢
	: , : , :
57	instantiation	71, 69, 65	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
61	instantiation	71, 66, 67	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
65	instantiation	71, 72, 68	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	71, 69, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
70	instantiation	71, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements