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	17	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7	⊢
	:
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 13, 28, 9, 10, 11^*	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
7	instantiation	12, 13, 14	⊢
	: , :
8	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
9	instantiation	67, 48, 15	⊢
	: , : , :
10	instantiation	16, 69	⊢
	:
11	instantiation	17, 18, 19	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
13	instantiation	67, 43, 20	⊢
	: , : , :
14	instantiation	30, 21	⊢
	:
15	instantiation	67, 54, 22	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	23, 33, 45, 62, 35, 34, 36, 37, 24	⊢
	: , : , : , : , : , :
19	instantiation	25, 45, 33, 34, 35, 36, 37, 31, 26^*	⊢
	: , : , : , : , :
20	instantiation	67, 48, 27	⊢
	: , : , :
21	instantiation	67, 43, 28	⊢
	: , : , :
22	instantiation	29, 55	⊢
	:
23	theorem		⊢
	proveit.numbers.multiplication.disassociation
24	instantiation	30, 31	⊢
	:
25	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
26	instantiation	32, 45, 33, 34, 35, 36, 37	⊢
	: , : , : , :
27	instantiation	67, 54, 38	⊢
	: , : , :
28	instantiation	67, 48, 39	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.negation.int_closure
30	theorem		⊢
	proveit.numbers.negation.complex_closure
31	instantiation	67, 43, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	instantiation	41	⊢
	: , :
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	67, 43, 42	⊢
	: , : , :
37	instantiation	67, 43, 44	⊢
	: , : , :
38	instantiation	67, 61, 45	⊢
	: , : , :
39	instantiation	67, 56, 46	⊢
	: , : , :
40	instantiation	67, 48, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
42	instantiation	67, 48, 49	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	50, 51, 60	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
46	instantiation	52, 57, 53	⊢
	: , :
47	instantiation	67, 54, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
49	instantiation	67, 56, 57	⊢
	: , : , :
50	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
51	instantiation	58, 59	⊢
	: , :
52	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
53	instantiation	67, 68, 60	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	instantiation	67, 61, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
57	instantiation	63, 64, 65	⊢
	: , :
58	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
60	assumption		⊢
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
64	instantiation	67, 68, 66	⊢
	: , : , :
65	instantiation	67, 68, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
^*equality replacement requirements