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	14	⊢
2	instantiation	22, 23, 4, 5, 6, 7	⊢
	: , : , : , :
3	instantiation	8, 9, 10, 11, 12^, 13^	⊢
	: , : , :
4	instantiation	33	⊢
	: , :
5	instantiation	33	⊢
	: , :
6	instantiation	14, 15, 16	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_3
8	theorem		⊢
	proveit.numbers.division.frac_cancel_left
9	instantiation	59, 18, 17	⊢
	: , : , :
10	instantiation	59, 18, 19	⊢
	: , : , :
11	instantiation	59, 44, 20	⊢
	: , : , :
12	instantiation	36, 21	⊢
	:
13	theorem		⊢
	proveit.numbers.numerals.decimals.mult_9_2
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	22, 23, 24, 25, 26, 27	⊢
	: , : , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_6
17	instantiation	59, 29, 28	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19	instantiation	59, 29, 30	⊢
	: , : , :
20	instantiation	59, 52, 31	⊢
	: , : , :
21	instantiation	59, 44, 32	⊢
	: , : , :
22	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
24	instantiation	33	⊢
	: , :
25	instantiation	33	⊢
	: , :
26	instantiation	34, 35	⊢
	:
27	instantiation	36, 37	⊢
	:
28	instantiation	59, 39, 38	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30	instantiation	59, 39, 40	⊢
	: , : , :
31	instantiation	59, 56, 41	⊢
	: , : , :
32	instantiation	59, 52, 42	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
35	instantiation	59, 44, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
37	instantiation	59, 44, 45	⊢
	: , : , :
38	instantiation	59, 47, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
40	instantiation	59, 47, 48	⊢
	: , : , :
41	instantiation	59, 60, 49	⊢
	: , : , :
42	instantiation	59, 56, 50	⊢
	: , : , :
43	instantiation	59, 52, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	59, 52, 53	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
50	instantiation	59, 60, 54	⊢
	: , : , :
51	instantiation	59, 56, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	59, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
55	instantiation	59, 60, 58	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
57	instantiation	59, 60, 61	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
59	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
^*equality replacement requirements