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	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5, 24, 6, 7^*	⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
4	instantiation	58, 37, 8	⊢
	: , : , :
5	instantiation	58, 41, 9	⊢
	: , : , :
6	instantiation	10, 60	⊢
	:
7	instantiation	11, 12, 13	⊢
	: , : , :
8	instantiation	58, 41, 14	⊢
	: , : , :
9	instantiation	58, 48, 15	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
11	axiom		⊢
	proveit.logic.equality.equals_transitivity
12	instantiation	16, 27, 32, 53, 29, 28, 30, 31, 17	⊢
	: , : , : , : , : , :
13	instantiation	18, 32, 27, 28, 29, 30, 31, 19, 20^*	⊢
	: , : , : , : , :
14	instantiation	58, 40, 21	⊢
	: , : , :
15	instantiation	22, 49, 23	⊢
	: , :
16	theorem		⊢
	proveit.numbers.multiplication.disassociation
17	instantiation	58, 37, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
19	instantiation	58, 37, 25	⊢
	: , : , :
20	instantiation	26, 32, 27, 28, 29, 30, 31	⊢
	: , : , : , :
21	instantiation	58, 52, 32	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
23	instantiation	58, 59, 45	⊢
	: , : , :
24	instantiation	58, 41, 33	⊢
	: , : , :
25	instantiation	58, 41, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	instantiation	35	⊢
	: , :
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	58, 37, 36	⊢
	: , : , :
31	instantiation	58, 37, 38	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
33	instantiation	58, 40, 39	⊢
	: , : , :
34	instantiation	58, 40, 47	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	instantiation	58, 41, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
38	instantiation	43, 44, 45	⊢
	: , : , :
39	instantiation	46, 47	⊢
	:
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	58, 48, 49	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
44	instantiation	50, 51	⊢
	: , :
45	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
46	theorem		⊢
	proveit.numbers.negation.int_closure
47	instantiation	58, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
49	instantiation	54, 55, 56	⊢
	: , :
50	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
54	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
55	instantiation	58, 59, 57	⊢
	: , : , :
56	instantiation	58, 59, 60	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
58	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
^*equality replacement requirements