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	23	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 49, 62, 7^*	⊢
	: , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 20, 19, 9^, 10^	⊢
	: , : , : , :
6	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
7	instantiation	23, 11, 12	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.division.prod_of_fracs
9	instantiation	44, 20	⊢
	:
10	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
11	instantiation	31, 32, 13, 14, 15, 16	⊢
	: , : , : , :
12	instantiation	17, 18, 19, 20, 21^, 22^	⊢
	: , : , :
13	instantiation	42	⊢
	: , :
14	instantiation	42	⊢
	: , :
15	instantiation	23, 24, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
17	theorem		⊢
	proveit.numbers.division.frac_cancel_left
18	instantiation	63, 27, 26	⊢
	: , : , :
19	instantiation	63, 27, 28	⊢
	: , : , :
20	instantiation	63, 51, 29	⊢
	: , : , :
21	instantiation	44, 30	⊢
	:
22	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	31, 32, 33, 34, 35, 36	⊢
	: , : , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
26	instantiation	63, 38, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
28	instantiation	63, 38, 39	⊢
	: , : , :
29	instantiation	63, 58, 40	⊢
	: , : , :
30	instantiation	63, 51, 41	⊢
	: , : , :
31	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
33	instantiation	42	⊢
	: , :
34	instantiation	42	⊢
	: , :
35	instantiation	43, 45	⊢
	:
36	instantiation	44, 45	⊢
	:
37	instantiation	63, 47, 46	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
39	instantiation	63, 47, 48	⊢
	: , : , :
40	instantiation	63, 61, 49	⊢
	: , : , :
41	instantiation	63, 58, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
44	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
45	instantiation	63, 51, 52	⊢
	: , : , :
46	instantiation	63, 54, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
48	instantiation	63, 54, 55	⊢
	: , : , :
49	instantiation	63, 64, 56	⊢
	: , : , :
50	instantiation	63, 61, 57	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
52	instantiation	63, 58, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
57	instantiation	63, 64, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	63, 61, 62	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements