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.numbers.addition.strong_bound_via_left_term_bound
2	reference	27	⊢
3	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
4	instantiation	62, 54, 8	⊢
	: , : , :
5	instantiation	9, 10	⊢
	:
6	instantiation	11, 12, 13	⊢
	: , : , :
7	instantiation	14, 15, 16, 17	⊢
	: , : , : , :
8	instantiation	62, 59, 18	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
11	theorem		⊢
	proveit.logic.equality.sub_right_side_into
12	instantiation	19, 21	⊢
	:
13	instantiation	20, 21, 22	⊢
	: , :
14	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
15	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_3
16	instantiation	23	⊢
	:
17	instantiation	24, 25	⊢
	: , :
18	instantiation	62, 63, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.elim_zero_right
20	theorem		⊢
	proveit.numbers.addition.commutation
21	instantiation	62, 47, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
23	axiom		⊢
	proveit.logic.equality.equals_reflexivity
24	theorem		⊢
	proveit.logic.equality.equals_reversal
25	instantiation	37, 38, 52, 39, 28, 29, 42, 30, 41, 31^*	⊢
	: , : , : , : , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
27	assumption		⊢
28	instantiation	45	⊢
	: , :
29	instantiation	45	⊢
	: , :
30	instantiation	62, 47, 32	⊢
	: , : , :
31	instantiation	49, 33, 34	⊢
	: , : , :
32	instantiation	62, 54, 35	⊢
	: , : , :
33	instantiation	56, 36	⊢
	: , : , :
34	instantiation	37, 38, 52, 64, 39, 40, 41, 42, 43^*	⊢
	: , : , : , : , : , :
35	instantiation	62, 59, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
37	theorem		⊢
	proveit.numbers.addition.association
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
40	instantiation	45	⊢
	: , :
41	instantiation	62, 47, 46	⊢
	: , : , :
42	instantiation	62, 47, 48	⊢
	: , : , :
43	instantiation	49, 50, 51	⊢
	: , : , :
44	instantiation	62, 63, 52	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	instantiation	62, 54, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	62, 54, 55	⊢
	: , : , :
49	axiom		⊢
	proveit.logic.equality.equals_transitivity
50	instantiation	56, 57	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.add_6_1
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
53	instantiation	62, 59, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
55	instantiation	62, 59, 60	⊢
	: , : , :
56	axiom		⊢
	proveit.logic.equality.substitution
57	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_3
58	instantiation	62, 63, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	62, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements