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	30	⊢
2	instantiation	7, 4	⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
4	instantiation	30, 5, 6	⊢
	: , : , :
5	instantiation	7, 8	⊢
	: , : , :
6	instantiation	9, 10, 72, 11, 12^*	⊢
	: , : , : , :
7	axiom		⊢
	proveit.logic.equality.substitution
8	instantiation	36, 13	⊢
	:
9	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
10	instantiation	73, 74, 14	⊢
	: , : , :
11	instantiation	73, 74, 15	⊢
	: , : , :
12	instantiation	30, 16, 17	⊢
	: , : , :
13	instantiation	73, 62, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
16	instantiation	41, 75, 19, 20, 21, 22	⊢
	: , : , : , :
17	instantiation	23, 24, 25, 55, 26^, 27^, 28^*	⊢
	: , : , :
18	instantiation	73, 68, 29	⊢
	: , : , :
19	instantiation	53	⊢
	: , :
20	instantiation	53	⊢
	: , :
21	instantiation	30, 31, 32	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
23	theorem		⊢
	proveit.numbers.division.frac_cancel_left
24	instantiation	73, 34, 33	⊢
	: , : , :
25	instantiation	73, 34, 35	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
27	instantiation	36, 37	⊢
	:
28	instantiation	38, 55	⊢
	:
29	instantiation	73, 39, 40	⊢
	: , : , :
30	axiom		⊢
	proveit.logic.equality.equals_transitivity
31	instantiation	41, 75, 42, 43, 44, 45	⊢
	: , : , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_6
33	instantiation	73, 47, 46	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
35	instantiation	73, 47, 48	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
37	instantiation	73, 62, 49	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.division.frac_one_denom
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
40	instantiation	50, 51, 52	⊢
	: , :
41	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
42	instantiation	53	⊢
	: , :
43	instantiation	53	⊢
	: , :
44	instantiation	54, 55	⊢
	:
45	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_3
46	instantiation	73, 57, 56	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
48	instantiation	73, 57, 58	⊢
	: , : , :
49	instantiation	73, 68, 59	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
51	instantiation	73, 60, 66	⊢
	: , : , :
52	instantiation	73, 60, 61	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
54	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
55	instantiation	73, 62, 63	⊢
	: , : , :
56	instantiation	73, 65, 64	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
58	instantiation	73, 65, 66	⊢
	: , : , :
59	instantiation	73, 71, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	73, 68, 69	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
67	instantiation	73, 74, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
69	instantiation	73, 71, 72	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	instantiation	73, 74, 75	⊢
	: , : , :
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements