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.addition.rational_pair_addition
2	reference	45	⊢
3	reference	61	⊢
4	reference	59	⊢
5	instantiation	18, 6, 7	⊢
	: , : , :
6	instantiation	26, 27, 8, 9, 10, 11	⊢
	: , : , : , :
7	instantiation	12, 13, 14, 15, 16^, 17^	⊢
	: , : , :
8	instantiation	37	⊢
	: , :
9	instantiation	37	⊢
	: , :
10	instantiation	18, 19, 20	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_3
12	theorem		⊢
	proveit.numbers.division.frac_cancel_left
13	instantiation	63, 22, 21	⊢
	: , : , :
14	instantiation	63, 22, 23	⊢
	: , : , :
15	instantiation	63, 48, 24	⊢
	: , : , :
16	instantiation	40, 25	⊢
	:
17	theorem		⊢
	proveit.numbers.numerals.decimals.mult_9_2
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	26, 27, 28, 29, 30, 31	⊢
	: , : , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_6
21	instantiation	63, 33, 32	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
23	instantiation	63, 33, 34	⊢
	: , : , :
24	instantiation	63, 56, 35	⊢
	: , : , :
25	instantiation	63, 48, 36	⊢
	: , : , :
26	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
28	instantiation	37	⊢
	: , :
29	instantiation	37	⊢
	: , :
30	instantiation	38, 39	⊢
	:
31	instantiation	40, 41	⊢
	:
32	instantiation	63, 43, 42	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
34	instantiation	63, 43, 44	⊢
	: , : , :
35	instantiation	63, 60, 45	⊢
	: , : , :
36	instantiation	63, 56, 46	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
39	instantiation	63, 48, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
41	instantiation	63, 48, 49	⊢
	: , : , :
42	instantiation	63, 51, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
44	instantiation	63, 51, 52	⊢
	: , : , :
45	instantiation	63, 64, 53	⊢
	: , : , :
46	instantiation	63, 60, 54	⊢
	: , : , :
47	instantiation	63, 56, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	63, 56, 57	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
54	instantiation	63, 64, 58	⊢
	: , : , :
55	instantiation	63, 60, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	63, 60, 61	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
59	instantiation	63, 64, 62	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	instantiation	63, 64, 65	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
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.nat6
^*equality replacement requirements