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, 6, 7^*	⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.addition.vec_sum_split_before
2	reference	46	⊢
3	reference	51	⊢
4	instantiation	52, 53, 8	⊢
	: , : , :
5	instantiation	19, 34, 20, 25, 9, 10^, 15^	⊢
	: , : , :
6	instantiation	11, 12	⊢
	: , :
7	instantiation	13, 14, 26, 38, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
9	instantiation	28, 16	⊢
	:
10	instantiation	30, 17, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.ordering.relax_less
12	instantiation	19, 44, 20, 21, 22, 23^, 24^	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
14	instantiation	52, 43, 25	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
16	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
17	instantiation	36, 26	⊢
	:
18	instantiation	37, 26, 39	⊢
	: , :
19	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
21	instantiation	52, 47, 27	⊢
	: , : , :
22	instantiation	28, 29	⊢
	:
23	instantiation	30, 31, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_5
25	instantiation	52, 47, 33	⊢
	: , : , :
26	instantiation	52, 43, 34	⊢
	: , : , :
27	instantiation	52, 50, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
30	theorem		⊢
	proveit.logic.equality.sub_right_side_into
31	instantiation	36, 38	⊢
	:
32	instantiation	37, 38, 39	⊢
	: , :
33	instantiation	52, 50, 40	⊢
	: , : , :
34	instantiation	52, 47, 41	⊢
	: , : , :
35	instantiation	52, 53, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.elim_zero_right
37	theorem		⊢
	proveit.numbers.addition.commutation
38	instantiation	52, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
40	instantiation	52, 53, 45	⊢
	: , : , :
41	instantiation	52, 50, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	52, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
46	instantiation	52, 53, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	52, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	52, 53, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
^*equality replacement requirements