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	31	⊢
3	instantiation	6	⊢
	: , :
4	instantiation	8, 7	⊢
	: , :
5	instantiation	8, 9	⊢
	: , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
7	instantiation	11, 40, 12, 10	⊢
	: , :
8	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
9	instantiation	11, 31, 12, 13	⊢
	: , :
10	instantiation	14, 33, 15, 16, 17, 18^, 19^	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
13	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
14	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
16	instantiation	38, 34, 20	⊢
	: , : , :
17	instantiation	21, 22	⊢
	:
18	instantiation	23, 24, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
20	instantiation	38, 36, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
23	theorem		⊢
	proveit.logic.equality.sub_right_side_into
24	instantiation	27, 29	⊢
	:
25	instantiation	28, 29, 30	⊢
	: , :
26	instantiation	38, 39, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.addition.elim_zero_right
28	theorem		⊢
	proveit.numbers.addition.commutation
29	instantiation	38, 32, 33	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	38, 34, 35	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	38, 36, 37	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	38, 39, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements