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	22	⊢
2	instantiation	24, 3, 4	⊢
	: , : , :
3	instantiation	22, 5	⊢
	: , : , :
4	instantiation	24, 6, 7	⊢
	: , : , :
5	instantiation	8, 33, 43, 9, 10^*	⊢
	: , :
6	instantiation	22, 11	⊢
	: , : , :
7	instantiation	12, 13	⊢
	: , :
8	theorem		⊢
	proveit.numbers.division.div_as_mult
9	instantiation	14, 86	⊢
	:
10	instantiation	24, 15, 16	⊢
	: , : , :
11	instantiation	17, 18, 49	⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.equals_reversal
13	instantiation	19, 43, 20, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
15	instantiation	22, 23	⊢
	: , : , :
16	instantiation	24, 25, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.commutation
18	instantiation	84, 56, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.product_of_pos_powers
20	instantiation	84, 28, 76	⊢
	: , : , :
21	instantiation	84, 28, 50	⊢
	: , : , :
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	29, 30, 83, 31^*	⊢
	: , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	32, 33, 49	⊢
	: , :
26	instantiation	34, 79, 77, 35, 36, 37, 49, 45, 46, 38^*	⊢
	: , : , : , : , : , :
27	instantiation	84, 66, 39	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
29	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
30	instantiation	84, 40, 41	⊢
	: , : , :
31	instantiation	42, 43	⊢
	:
32	theorem		⊢
	proveit.numbers.multiplication.commutation
33	instantiation	44, 45, 46	⊢
	: , :
34	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
35	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
36	instantiation	47	⊢
	: , :
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	instantiation	48, 49	⊢
	:
39	instantiation	84, 75, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
41	instantiation	84, 51, 52	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
43	instantiation	84, 56, 53	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
45	instantiation	84, 56, 54	⊢
	: , : , :
46	instantiation	84, 56, 55	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
49	instantiation	84, 56, 57	⊢
	: , : , :
50	instantiation	58, 76, 59	⊢
	: , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
52	instantiation	84, 60, 61	⊢
	: , : , :
53	instantiation	84, 66, 62	⊢
	: , : , :
54	instantiation	63, 64, 68	⊢
	: , : , :
55	instantiation	84, 66, 65	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	84, 66, 67	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
59	instantiation	84, 85, 68	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
61	instantiation	84, 69, 86	⊢
	: , : , :
62	instantiation	84, 73, 70	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
64	instantiation	71, 72	⊢
	: , :
65	instantiation	84, 73, 74	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	84, 75, 76	⊢
	: , : , :
68	assumption		⊢
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
70	instantiation	84, 78, 77	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	instantiation	84, 78, 79	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
76	instantiation	80, 81, 82	⊢
	: , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
78	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
80	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
81	instantiation	84, 85, 83	⊢
	: , : , :
82	instantiation	84, 85, 86	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
84	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
86	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
^*equality replacement requirements