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	9	⊢
2	instantiation	4, 33, 5, 6, 7	⊢
	: , : , :
3	assumption		⊢
4	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
5	instantiation	8	⊢
	: , :
6	instantiation	9, 10, 11	⊢
	: , : , :
7	instantiation	14, 42, 12, 13	⊢
	: , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	14, 42, 33, 15	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
13	instantiation	16, 35, 17, 18, 19, 20^, 21^	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
15	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
16	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
18	instantiation	40, 36, 22	⊢
	: , : , :
19	instantiation	23, 24	⊢
	:
20	instantiation	25, 26, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
22	instantiation	40, 38, 28	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
25	theorem		⊢
	proveit.logic.equality.sub_right_side_into
26	instantiation	29, 31	⊢
	:
27	instantiation	30, 31, 32	⊢
	: , :
28	instantiation	40, 41, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.elim_zero_right
30	theorem		⊢
	proveit.numbers.addition.commutation
31	instantiation	40, 34, 35	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	40, 36, 37	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	40, 38, 39	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	40, 41, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements