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, 4, 5^*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.division.div_as_mult
2	instantiation	6, 44, 7, 8	⊢
	: , :
3	reference	37	⊢
4	instantiation	12, 64	⊢
	:
5	instantiation	23, 9, 10	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.division.div_complex_closure
7	instantiation	68, 50, 11	⊢
	: , : , :
8	instantiation	12, 66	⊢
	:
9	instantiation	13, 14	⊢
	: , : , :
10	instantiation	15, 44, 16, 36, 35, 17^*	⊢
	: , : , : , :
11	instantiation	68, 56, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
13	axiom		⊢
	proveit.logic.equality.substitution
14	instantiation	19, 35, 20, 21^*	⊢
	: , :
15	theorem		⊢
	proveit.numbers.division.prod_of_fracs
16	instantiation	68, 50, 22	⊢
	: , : , :
17	instantiation	23, 24, 25	⊢
	: , : , :
18	instantiation	68, 62, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
21	instantiation	27, 37	⊢
	:
22	instantiation	68, 56, 28	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	29, 67, 30, 31, 32, 33	⊢
	: , : , : , :
25	instantiation	34, 35, 36, 37, 38^, 39^	⊢
	: , : , :
26	instantiation	68, 69, 40	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
28	instantiation	68, 62, 41	⊢
	: , : , :
29	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
30	instantiation	42	⊢
	: , :
31	instantiation	42	⊢
	: , :
32	instantiation	43, 44	⊢
	:
33	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_2
34	theorem		⊢
	proveit.numbers.division.frac_cancel_left
35	instantiation	68, 46, 45	⊢
	: , : , :
36	instantiation	68, 46, 47	⊢
	: , : , :
37	instantiation	68, 50, 48	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
39	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_3
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
41	instantiation	68, 69, 49	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
44	instantiation	68, 50, 51	⊢
	: , : , :
45	instantiation	68, 53, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
47	instantiation	68, 53, 54	⊢
	: , : , :
48	instantiation	68, 56, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	68, 56, 57	⊢
	: , : , :
52	instantiation	68, 59, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
54	instantiation	68, 59, 60	⊢
	: , : , :
55	instantiation	68, 62, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	68, 62, 63	⊢
	: , : , :
58	instantiation	68, 65, 64	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
60	instantiation	68, 65, 66	⊢
	: , : , :
61	instantiation	68, 69, 67	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
63	instantiation	68, 69, 70	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements