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	11	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 41, 42, 43, 9^, 10^	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	11, 12, 13	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
7	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
8	instantiation	14	⊢
	: , : , :
9	instantiation	16, 15	⊢
	:
10	instantiation	16, 17	⊢
	:
11	axiom		⊢
	proveit.logic.equality.equals_transitivity
12	instantiation	18, 37, 58, 38, 39, 19, 22, 42, 20	⊢
	: , : , : , : , : , :
13	instantiation	21, 42, 22, 23	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
15	instantiation	24, 58	⊢
	:
16	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
17	instantiation	25, 26	⊢
	: , :
18	theorem		⊢
	proveit.numbers.addition.disassociation
19	instantiation	45	⊢
	: , :
20	instantiation	56, 48, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
22	instantiation	56, 48, 28	⊢
	: , : , :
23	instantiation	29	⊢
	:
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
25	theorem		⊢
	proveit.numbers.ordering.relax_less
26	instantiation	30, 53	⊢
	:
27	instantiation	31, 47	⊢
	:
28	instantiation	32, 33, 34	⊢
	: , : , :
29	axiom		⊢
	proveit.logic.equality.equals_reflexivity
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
31	theorem		⊢
	proveit.numbers.negation.real_closure
32	theorem		⊢
	proveit.logic.equality.sub_right_side_into
33	instantiation	44, 35, 49	⊢
	: , :
34	instantiation	36, 37, 58, 38, 39, 40, 41, 42, 43	⊢
	: , : , : , : , : , :
35	instantiation	44, 46, 47	⊢
	: , :
36	theorem		⊢
	proveit.numbers.multiplication.disassociation
37	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
39	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
40	instantiation	45	⊢
	: , :
41	instantiation	56, 48, 46	⊢
	: , : , :
42	instantiation	56, 48, 47	⊢
	: , : , :
43	instantiation	56, 48, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	instantiation	56, 50, 51	⊢
	: , : , :
47	instantiation	56, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	56, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
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.nat2
^*equality replacement requirements