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	⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
2	reference	49	⊢
3	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
4	reference	8	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	7, 49, 8, 9, 10	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
8	instantiation	11	⊢
	: , :
9	instantiation	12, 13	⊢
	: , :
10	instantiation	16, 46, 14, 15	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
13	instantiation	16, 49, 46, 17	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
15	instantiation	20, 37, 21, 39, 22, 18^, 19^	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
17	instantiation	20, 39, 21, 22, 23^, 24^	⊢
	: , : , :
18	instantiation	29, 25, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_4
20	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
22	instantiation	27, 28	⊢
	:
23	instantiation	29, 30, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
25	instantiation	33, 32	⊢
	:
26	instantiation	34, 32, 36	⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
29	theorem		⊢
	proveit.logic.equality.sub_right_side_into
30	instantiation	33, 35	⊢
	:
31	instantiation	34, 35, 36	⊢
	: , :
32	instantiation	47, 38, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.elim_zero_right
34	theorem		⊢
	proveit.numbers.addition.commutation
35	instantiation	47, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
37	instantiation	47, 41, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	47, 41, 42	⊢
	: , : , :
40	instantiation	47, 44, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	47, 44, 45	⊢
	: , : , :
43	instantiation	47, 48, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
45	instantiation	47, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements