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	⊢
	: , : , :
1	reference	38	⊢
2	instantiation	44, 4	⊢
	: , : , :
3	instantiation	5, 6, 7, 8	⊢
	: , : , : , :
4	instantiation	38, 9, 10	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
6	instantiation	11, 12, 32	⊢
	: , :
7	instantiation	13, 49, 14, 15, 16	⊢
	: , : , : , :
8	instantiation	26, 27, 52, 29, 17, 32, 18^*	⊢
	: , : , : , : , : , :
9	instantiation	44, 19	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
11	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_expansion
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
13	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
14	instantiation	20, 49	⊢
	: , :
15	instantiation	21	⊢
	: , : , : , :
16	instantiation	22	⊢
	:
17	instantiation	34	⊢
	: , :
18	instantiation	38, 23, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
20	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
22	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_4_repeats
23	instantiation	44, 25	⊢
	: , : , :
24	instantiation	26, 27, 52, 28, 29, 30, 31, 32, 33^*	⊢
	: , : , : , : , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
26	theorem		⊢
	proveit.numbers.multiplication.association
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	34	⊢
	: , :
31	instantiation	50, 36, 35	⊢
	: , : , :
32	instantiation	50, 36, 37	⊢
	: , : , :
33	instantiation	38, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35	instantiation	50, 42, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	50, 42, 43	⊢
	: , : , :
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
41	instantiation	50, 47, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	50, 47, 48	⊢
	: , : , :
44	axiom		⊢
	proveit.logic.equality.substitution
45	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
46	instantiation	50, 51, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	50, 51, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements