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, 9, 10^*	⊢
	: , : , : , : , : , :
1	reference	16	⊢
2	reference	17	⊢
3	reference	31	⊢
4	reference	18	⊢
5	instantiation	24	⊢
	: , :
6	instantiation	24	⊢
	: , :
7	reference	21	⊢
8	instantiation	41, 26, 11	⊢
	: , : , :
9	reference	20	⊢
10	instantiation	28, 12, 13	⊢
	: , : , :
11	instantiation	41, 33, 14	⊢
	: , : , :
12	instantiation	35, 15	⊢
	: , : , :
13	instantiation	16, 17, 31, 43, 18, 19, 20, 21, 22^*	⊢
	: , : , : , : , : , :
14	instantiation	41, 38, 23	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
16	theorem		⊢
	proveit.numbers.addition.association
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19	instantiation	24	⊢
	: , :
20	instantiation	41, 26, 25	⊢
	: , : , :
21	instantiation	41, 26, 27	⊢
	: , : , :
22	instantiation	28, 29, 30	⊢
	: , : , :
23	instantiation	41, 42, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25	instantiation	41, 33, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
27	instantiation	41, 33, 34	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	35, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.add_6_1
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
32	instantiation	41, 38, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	41, 38, 39	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.substitution
36	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_3
37	instantiation	41, 42, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	41, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements