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	36	⊢
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, 36, 8, 9, 10	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
8	instantiation	11	⊢
	: , :
9	instantiation	13, 12	⊢
	: , :
10	instantiation	13, 14	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	instantiation	16, 45, 17, 15	⊢
	: , :
13	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
14	instantiation	16, 36, 17, 18	⊢
	: , :
15	instantiation	19, 38, 20, 21, 22, 23^, 24^	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
18	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
19	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
21	instantiation	43, 39, 25	⊢
	: , : , :
22	instantiation	26, 27	⊢
	:
23	instantiation	28, 29, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
25	instantiation	43, 41, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
28	theorem		⊢
	proveit.logic.equality.sub_right_side_into
29	instantiation	32, 34	⊢
	:
30	instantiation	33, 34, 35	⊢
	: , :
31	instantiation	43, 44, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.addition.elim_zero_right
33	theorem		⊢
	proveit.numbers.addition.commutation
34	instantiation	43, 37, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
38	instantiation	43, 39, 40	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	43, 41, 42	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements