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	29, 4	⊢
	: , : , :
3	instantiation	24, 5, 6	⊢
	: , : , :
4	instantiation	29, 7	⊢
	: , : , :
5	instantiation	8, 9, 76, 10, 11, 12, 15, 13, 16	⊢
	: , : , : , : , : , :
6	instantiation	14, 15, 16, 17	⊢
	: , : , :
7	instantiation	18, 32, 47, 51, 19^*	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.disassociation
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	instantiation	20	⊢
	: , :
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	74, 54, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
15	instantiation	74, 54, 27	⊢
	: , : , :
16	instantiation	74, 54, 22	⊢
	: , : , :
17	instantiation	23	⊢
	:
18	theorem		⊢
	proveit.numbers.division.div_as_mult
19	instantiation	24, 25, 26	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	instantiation	42, 27	⊢
	:
22	instantiation	28, 41, 50	⊢
	: , :
23	axiom		⊢
	proveit.logic.equality.equals_reflexivity
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	29, 30	⊢
	: , : , :
26	instantiation	31, 32, 33	⊢
	: , :
27	instantiation	34, 35, 36, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
29	axiom		⊢
	proveit.logic.equality.substitution
30	instantiation	38, 39, 71, 40^*	⊢
	: , :
31	theorem		⊢
	proveit.numbers.multiplication.commutation
32	instantiation	74, 54, 50	⊢
	: , : , :
33	instantiation	74, 54, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
35	instantiation	42, 43	⊢
	:
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
39	instantiation	74, 44, 45	⊢
	: , : , :
40	instantiation	46, 47	⊢
	:
41	instantiation	74, 63, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.negation.real_closure
43	instantiation	49, 50, 55, 51	⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
45	instantiation	74, 52, 53	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
47	instantiation	74, 54, 55	⊢
	: , : , :
48	instantiation	74, 56, 57	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.division.div_real_closure
50	instantiation	74, 58, 59	⊢
	: , : , :
51	instantiation	60, 73	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
53	instantiation	74, 61, 62	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	74, 63, 64	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
57	instantiation	65, 66, 67	⊢
	: , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
60	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
62	instantiation	74, 68, 73	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
64	instantiation	74, 69, 70	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
66	instantiation	74, 72, 71	⊢
	: , : , :
67	instantiation	74, 72, 73	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
70	instantiation	74, 75, 76	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
73	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
74	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements