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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
2	reference	44	⊢
3	instantiation	6	⊢
	: , :
4	instantiation	7, 8	⊢
	: , :
5	instantiation	9, 10, 19	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
7	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
8	instantiation	12, 44, 41, 11	⊢
	: , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	12, 41, 13, 14	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
12	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
14	instantiation	15, 32, 16, 34, 17, 18^, 19^	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
17	instantiation	20, 21	⊢
	:
18	instantiation	24, 22, 23	⊢
	: , : , :
19	instantiation	24, 25, 26	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
22	instantiation	27, 30	⊢
	:
23	instantiation	29, 30, 28	⊢
	: , :
24	theorem		⊢
	proveit.logic.equality.sub_right_side_into
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_2
26	instantiation	29, 30, 31	⊢
	: , :
27	theorem		⊢
	proveit.numbers.addition.elim_zero_right
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
29	theorem		⊢
	proveit.numbers.addition.commutation
30	instantiation	42, 33, 32	⊢
	: , : , :
31	instantiation	42, 33, 34	⊢
	: , : , :
32	instantiation	42, 36, 35	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	42, 36, 37	⊢
	: , : , :
35	instantiation	42, 39, 38	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	42, 39, 40	⊢
	: , : , :
38	instantiation	42, 43, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	42, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements