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