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^*	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_equiv
2	reference	64	⊢
3	instantiation	14	⊢
	: , : , :
4	instantiation	24, 5, 6	⊢
	: , : , :
5	instantiation	7, 64, 8, 9, 10, 11, 12	⊢
	: , : , : , :
6	instantiation	34, 13	⊢
	:
7	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
8	instantiation	14	⊢
	: , : , :
9	instantiation	14	⊢
	: , : , :
10	instantiation	17, 15^*	⊢
	: , :
11	instantiation	17, 16^*	⊢
	: , :
12	instantiation	17, 18^*	⊢
	: , :
13	instantiation	19, 73, 20	⊢
	: , : , : , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
15	instantiation	24, 21, 26	⊢
	: , : , :
16	instantiation	22, 23	⊢
	:
17	axiom		⊢
	proveit.logic.equality.not_equals_def
18	instantiation	24, 25, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.logic.booleans.conjunction.nand_if_not_one
20	theorem		⊢
	proveit.logic.booleans.negation.not_false
21	instantiation	30, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.logic.booleans.negation.falsified_negation_intro
23	instantiation	28, 29	⊢
	: , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	30, 31	⊢
	: , : , :
26	axiom		⊢
	proveit.logic.booleans.negation.not_f
27	instantiation	34, 32	⊢
	:
28	theorem		⊢
	proveit.logic.equality.equals_reversal
29	instantiation	56, 52, 33	⊢
	: , : , :
30	axiom		⊢
	proveit.logic.equality.substitution
31	instantiation	34, 35	⊢
	:
32	instantiation	38, 36	⊢
	: , :
33	instantiation	61, 37, 62	⊢
	: , :
34	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
35	instantiation	38, 39	⊢
	: , :
36	instantiation	41, 40	⊢
	: , :
37	instantiation	71, 65, 49	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.equality.unfold_not_equals
39	instantiation	41, 42	⊢
	: , :
40	instantiation	44, 73, 45, 43	⊢
	: , :
41	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
42	instantiation	44, 64, 45, 46	⊢
	: , :
43	instantiation	47, 66, 48, 49, 50, 51^, 52^	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
46	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
47	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
49	instantiation	71, 67, 53	⊢
	: , : , :
50	instantiation	54, 55	⊢
	:
51	instantiation	56, 57, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
53	instantiation	71, 69, 59	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
55	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
56	theorem		⊢
	proveit.logic.equality.sub_right_side_into
57	instantiation	60, 62	⊢
	:
58	instantiation	61, 62, 63	⊢
	: , :
59	instantiation	71, 72, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.elim_zero_right
61	theorem		⊢
	proveit.numbers.addition.commutation
62	instantiation	71, 65, 66	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
66	instantiation	71, 67, 68	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
68	instantiation	71, 69, 70	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
70	instantiation	71, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements