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