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.equality.equals_reversal
2	instantiation	3, 47, 49, 4, 5, 6, 7^*	⊢
	: , : , : , : , :
3	theorem		⊢
	proveit.numbers.summation.sum_split_before
4	instantiation	51, 52, 8	⊢
	: , : , :
5	instantiation	9, 38, 13, 30, 10, 11^, 20^	⊢
	: , : , :
6	instantiation	12, 41, 13, 14, 15, 16^, 17^	⊢
	: , : , :
7	instantiation	18, 19, 31, 35, 20	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
9	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
10	instantiation	21, 22	⊢
	:
11	instantiation	27, 23, 24	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
14	instantiation	51, 44, 25	⊢
	: , : , :
15	instantiation	26, 39	⊢
	:
16	instantiation	27, 28, 29	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_6
18	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
19	instantiation	51, 40, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_1
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
23	instantiation	33, 31	⊢
	:
24	instantiation	34, 31, 36	⊢
	: , :
25	instantiation	51, 48, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
27	theorem		⊢
	proveit.logic.equality.sub_right_side_into
28	instantiation	33, 35	⊢
	:
29	instantiation	34, 35, 36	⊢
	: , :
30	instantiation	51, 44, 37	⊢
	: , : , :
31	instantiation	51, 40, 38	⊢
	: , : , :
32	instantiation	51, 52, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.elim_zero_right
34	theorem		⊢
	proveit.numbers.addition.commutation
35	instantiation	51, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
37	instantiation	51, 48, 42	⊢
	: , : , :
38	instantiation	51, 44, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	51, 44, 45	⊢
	: , : , :
42	instantiation	51, 52, 46	⊢
	: , : , :
43	instantiation	51, 48, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	51, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
47	instantiation	51, 52, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	51, 52, 53	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
^*equality replacement requirements