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, 7	⊢
	: , : , : , :
1	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
3	instantiation	8	⊢
	: , : , : , : , :
4	instantiation	8	⊢
	: , : , : , : , :
5	instantiation	9, 10, 11	⊢
	: , : , :
6	instantiation	12, 24, 22, 13	⊢
	: , : , :
7	instantiation	12, 24, 23, 13	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	14, 19, 18, 21, 20, 15, 22, 23, 16, 24	⊢
	: , : , : , : , : , :
11	instantiation	17, 18, 19, 20, 21, 22, 23, 24	⊢
	: , : , : , : , : , : , : , :
12	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
13	instantiation	25	⊢
	:
14	theorem		⊢
	proveit.numbers.addition.disassociation
15	instantiation	27	⊢
	: , :
16	instantiation	45, 30, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
19	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
20	instantiation	27	⊢
	: , :
21	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22	instantiation	45, 30, 28	⊢
	: , : , :
23	instantiation	45, 30, 29	⊢
	: , : , :
24	instantiation	45, 30, 31	⊢
	: , : , :
25	axiom		⊢
	proveit.logic.equality.equals_reflexivity
26	instantiation	45, 37, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	34, 35, 33	⊢
	: , : , :
29	instantiation	34, 35, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	45, 37, 38	⊢
	: , : , :
32	instantiation	45, 42, 39	⊢
	: , : , :
33	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
34	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
35	instantiation	40, 41	⊢
	: , :
36	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	45, 42, 44	⊢
	: , : , :
39	instantiation	43, 44	⊢
	:
40	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	theorem		⊢
	proveit.numbers.negation.int_closure
44	instantiation	45, 46, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1