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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 41, 51, 7, 9, 8, 5, 10, 11	⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 51, 8, 9, 10, 11	⊢
	: , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.disassociation
5	instantiation	49, 21, 12	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	13	⊢
	: , :
10	instantiation	49, 21, 14	⊢
	: , : , :
11	instantiation	15, 16, 17	⊢
	: , :
12	instantiation	49, 26, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	instantiation	49, 26, 19	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
16	instantiation	49, 21, 20	⊢
	: , : , :
17	instantiation	49, 21, 22	⊢
	: , : , :
18	instantiation	49, 32, 39	⊢
	: , : , :
19	instantiation	49, 23, 24	⊢
	: , : , :
20	instantiation	49, 26, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
22	instantiation	49, 26, 27	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
24	instantiation	28, 29, 30	⊢
	: , :
25	instantiation	49, 32, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
27	instantiation	49, 32, 44	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
29	instantiation	49, 34, 33	⊢
	: , : , :
30	instantiation	49, 34, 35	⊢
	: , : , :
31	instantiation	49, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
36	instantiation	38, 39, 40	⊢
	: , :
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
39	instantiation	49, 50, 41	⊢
	: , : , :
40	instantiation	42, 43, 44	⊢
	: , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
42	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
43	instantiation	49, 45, 46	⊢
	: , : , :
44	instantiation	47, 48	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
46	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
47	theorem		⊢
	proveit.numbers.negation.int_closure
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2