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^*	⊢
	: , : , : , : , : , :
1	reference	19	⊢
2	reference	45	⊢
3	reference	16	⊢
4	reference	20	⊢
5	instantiation	27	⊢
	: , : , :
6	reference	22	⊢
7	instantiation	43, 31, 10	⊢
	: , : , :
8	reference	29	⊢
9	instantiation	11, 12, 13^*	⊢
	: , :
10	instantiation	43, 37, 14	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	15, 20, 16, 45, 22, 17, 24, 29, 18^*	⊢
	: , : , : , : , : , :
13	instantiation	19, 20, 21, 45, 22, 23, 24, 25^*	⊢
	: , : , : , : , : , :
14	instantiation	43, 41, 26	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
17	instantiation	27	⊢
	: , : , :
18	instantiation	28, 29	⊢
	:
19	theorem		⊢
	proveit.numbers.addition.association
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	instantiation	30	⊢
	: , :
24	instantiation	43, 31, 32	⊢
	: , : , :
25	instantiation	33, 34, 35	⊢
	: , : , :
26	instantiation	43, 44, 36	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
28	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
29	assumption		⊢
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	43, 37, 38	⊢
	: , : , :
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat7
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	43, 41, 42	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.substitution
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements