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, 26, 22, 13	⊢
	: , : , :
7	instantiation	12, 26, 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, 26	⊢
	: , : , : , : , : , :
11	instantiation	17, 18, 19, 20, 21, 22, 23, 26	⊢
	: , : , : , : , : , : , : , :
12	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
13	instantiation	24	⊢
	:
14	theorem		⊢
	proveit.numbers.addition.disassociation
15	instantiation	27	⊢
	: , :
16	instantiation	25, 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	42, 30, 28	⊢
	: , : , :
23	instantiation	42, 30, 29	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_reflexivity
25	theorem		⊢
	proveit.numbers.negation.complex_closure
26	instantiation	42, 30, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	33, 34, 32	⊢
	: , : , :
29	instantiation	33, 34, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	42, 36, 37	⊢
	: , : , :
32	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
33	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
34	instantiation	38, 39	⊢
	: , :
35	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	42, 40, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	42, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1