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