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	21	⊢
2	instantiation	4, 61, 5, 6, 7, 8, 9	⊢
	: , : , : , :
3	instantiation	31, 10	⊢
	:
4	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
5	instantiation	11	⊢
	: , : , :
6	instantiation	11	⊢
	: , : , :
7	instantiation	14, 12^*	⊢
	: , :
8	instantiation	14, 13^*	⊢
	: , :
9	instantiation	14, 15^*	⊢
	: , :
10	instantiation	16, 70, 17	⊢
	: , : , : , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
12	instantiation	21, 18, 23	⊢
	: , : , :
13	instantiation	19, 20	⊢
	:
14	axiom		⊢
	proveit.logic.equality.not_equals_def
15	instantiation	21, 22, 23	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.booleans.conjunction.nand_if_not_one
17	theorem		⊢
	proveit.logic.booleans.negation.not_false
18	instantiation	27, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.logic.booleans.negation.falsified_negation_intro
20	instantiation	25, 26	⊢
	: , :
21	axiom		⊢
	proveit.logic.equality.equals_transitivity
22	instantiation	27, 28	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.booleans.negation.not_f
24	instantiation	31, 29	⊢
	:
25	theorem		⊢
	proveit.logic.equality.equals_reversal
26	instantiation	53, 49, 30	⊢
	: , : , :
27	axiom		⊢
	proveit.logic.equality.substitution
28	instantiation	31, 32	⊢
	:
29	instantiation	35, 33	⊢
	: , :
30	instantiation	58, 34, 59	⊢
	: , :
31	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
32	instantiation	35, 36	⊢
	: , :
33	instantiation	38, 37	⊢
	: , :
34	instantiation	68, 62, 46	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.unfold_not_equals
36	instantiation	38, 39	⊢
	: , :
37	instantiation	41, 70, 42, 40	⊢
	: , :
38	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
39	instantiation	41, 61, 42, 43	⊢
	: , :
40	instantiation	44, 63, 45, 46, 47, 48^, 49^	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
43	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
44	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
46	instantiation	68, 64, 50	⊢
	: , : , :
47	instantiation	51, 52	⊢
	:
48	instantiation	53, 54, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
50	instantiation	68, 66, 56	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
53	theorem		⊢
	proveit.logic.equality.sub_right_side_into
54	instantiation	57, 59	⊢
	:
55	instantiation	58, 59, 60	⊢
	: , :
56	instantiation	68, 69, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.elim_zero_right
58	theorem		⊢
	proveit.numbers.addition.commutation
59	instantiation	68, 62, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	68, 64, 65	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	68, 66, 67	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	68, 69, 70	⊢
	: , : , :
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.nat1
^*equality replacement requirements