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	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	4, 47, 5, 6, 7, 8, 9^*	, ⊢
	: , : , :
3	instantiation	10, 38, 11, 22, 12^*	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
5	instantiation	75, 58, 13	, ⊢
	: , : , :
6	instantiation	75, 58, 14	⊢
	: , : , :
7	instantiation	15, 41, 42, 33	, ⊢
	: , : , :
8	instantiation	16, 63	⊢
	:
9	instantiation	17, 18, 19	, ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
11	instantiation	75, 46, 20	⊢
	: , : , :
12	instantiation	21, 38, 22	⊢
	:
13	instantiation	75, 66, 23	, ⊢
	: , : , :
14	instantiation	75, 66, 42	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
16	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	24, 25, 26, 29, 27^*	, ⊢
	: , : , :
19	instantiation	28, 29	⊢
	:
20	instantiation	75, 58, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
22	instantiation	31, 63	⊢
	:
23	instantiation	75, 32, 33	, ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.division.frac_cancel_left
25	instantiation	75, 35, 34	⊢
	: , : , :
26	instantiation	75, 35, 36	⊢
	: , : , :
27	instantiation	37, 38	⊢
	:
28	theorem		⊢
	proveit.numbers.division.frac_one_denom
29	instantiation	75, 46, 39	⊢
	: , : , :
30	instantiation	75, 66, 62	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
32	instantiation	40, 41, 42	⊢
	: , :
33	instantiation	48, 68, 52	⊢
	: , : , : , : , :
34	instantiation	75, 44, 43	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
36	instantiation	75, 44, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
38	instantiation	75, 46, 47	⊢
	: , : , :
39	instantiation	48, 49, 74, 50, 51, 52	⊢
	: , : , : , : , :
40	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
41	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
42	instantiation	53, 67, 54	⊢
	: , :
43	instantiation	75, 56, 55	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
45	instantiation	75, 56, 57	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	75, 58, 59	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
49	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
50	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
51	instantiation	60	⊢
	: , :
52	assumption		⊢
53	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
54	instantiation	61, 62	⊢
	:
55	instantiation	75, 64, 63	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	75, 64, 65	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	75, 66, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
61	theorem		⊢
	proveit.numbers.negation.int_closure
62	instantiation	75, 73, 68	⊢
	: , : , :
63	instantiation	69, 74, 72	⊢
	: , :
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	70, 71, 72	⊢
	: , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
70	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
71	instantiation	75, 73, 74	⊢
	: , : , :
72	instantiation	75, 76, 77	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
77	assumption		⊢
^*equality replacement requirements