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, 8^*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.general_len
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
3	instantiation	20	⊢
	: , : , : , :
4	instantiation	20	⊢
	: , : , : , :
5	reference	15	⊢
6	instantiation	9, 58, 16	⊢
	: , : , :
7	instantiation	9, 41, 17	⊢
	: , : , :
8	instantiation	45, 10, 11	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	12, 13, 14, 15, 16, 17	⊢
	: , : , : , :
11	instantiation	45, 18, 19	⊢
	: , : , :
12	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
14	instantiation	20	⊢
	: , : , : , :
15	instantiation	20	⊢
	: , : , : , :
16	instantiation	21, 37, 23	⊢
	: , : , :
17	instantiation	22, 37, 27, 23	⊢
	: , : , :
18	instantiation	24, 34, 58, 33, 36, 35, 37, 27	⊢
	: , : , : , : , : , : , :
19	instantiation	32, 33, 25, 58, 35, 26, 37, 27, 28^*	⊢
	: , : , : , : , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
21	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
22	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
23	instantiation	29	⊢
	:
24	theorem		⊢
	proveit.numbers.addition.leftward_commutation
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
26	instantiation	30	⊢
	: , : , :
27	instantiation	56, 43, 31	⊢
	: , : , :
28	instantiation	32, 33, 34, 58, 35, 36, 37, 38^*	⊢
	: , : , : , : , : , :
29	axiom		⊢
	proveit.logic.equality.equals_reflexivity
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
31	instantiation	39, 40, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.addition.association
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	42	⊢
	: , :
37	instantiation	56, 43, 44	⊢
	: , : , :
38	instantiation	45, 46, 47	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
40	instantiation	48, 49	⊢
	: , :
41	assumption		⊢
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	56, 50, 51	⊢
	: , : , :
45	axiom		⊢
	proveit.logic.equality.equals_transitivity
46	instantiation	52, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
48	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	56, 54, 55	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.substitution
53	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	instantiation	56, 57, 58	⊢
	: , : , :
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements