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, 11^*	, , ⊢
	: , : , : , : , : , :
1	reference	20	⊢
2	reference	21	⊢
3	reference	17	⊢
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
5	reference	23	⊢
6	instantiation	27	⊢
	: , : , :
7	instantiation	12	⊢
	: , : , : , :
8	reference	29	⊢
9	assumption		⊢
10	assumption		⊢
11	instantiation	13, 14, 15^*	⊢
	: , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	16, 21, 17, 44, 23, 18, 25, 29, 19^*	⊢
	: , : , : , : , : , :
15	instantiation	20, 21, 22, 44, 23, 24, 25, 26^*	⊢
	: , : , : , : , : , :
16	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
18	instantiation	27	⊢
	: , : , :
19	instantiation	28, 29	⊢
	:
20	theorem		⊢
	proveit.numbers.addition.association
21	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	30	⊢
	: , :
25	instantiation	42, 31, 32	⊢
	: , : , :
26	instantiation	33, 34, 35	⊢
	: , : , :
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	42, 36, 37	⊢
	: , : , :
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	38, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	42, 40, 41	⊢
	: , : , :
38	axiom		⊢
	proveit.logic.equality.substitution
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	42, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements