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	⊢
	: , :
1	theorem		⊢
	proveit.logic.sets.membership.unfold_not_in_set
2	instantiation	3, 42, 4, 5, 6	⊢
	: , : , :
3	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
4	instantiation	7	⊢
	: , :
5	instantiation	10, 42, 8, 9	⊢
	: , :
6	instantiation	10, 42, 11, 12	⊢
	: , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
9	instantiation	15, 35, 16, 13, 19^, 14^	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
12	instantiation	15, 35, 16, 17, 18, 19^, 20^	⊢
	: , : , :
13	instantiation	23, 21	⊢
	:
14	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
15	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
17	instantiation	40, 36, 22	⊢
	: , : , :
18	instantiation	23, 24	⊢
	:
19	instantiation	25, 26, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_2
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
22	instantiation	40, 38, 28	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
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.nat3
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.nat2
^*equality replacement requirements