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, 8^*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.modular.redundant_mod_elimination_in_sum_in_modabs
2	reference	19	⊢
3	reference	55	⊢
4	reference	20	⊢
5	instantiation	56, 40, 9	⊢
	: , : , :
6	reference	31	⊢
7	instantiation	56, 10, 11	⊢
	: , : , :
8	instantiation	12, 13, 14	⊢
	: , : , :
9	instantiation	56, 43, 15	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
11	instantiation	56, 16, 17	⊢
	: , : , :
12	axiom		⊢
	proveit.logic.equality.equals_transitivity
13	instantiation	18, 19, 28, 55, 20, 21, 24, 25, 22	⊢
	: , : , : , : , : , :
14	instantiation	23, 24, 25, 26	⊢
	: , : , :
15	instantiation	49, 44, 42	⊢
	: , :
16	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
17	instantiation	27, 28, 29	⊢
	: , :
18	theorem		⊢
	proveit.numbers.addition.disassociation
19	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
20	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
21	instantiation	30	⊢
	: , :
22	instantiation	56, 32, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
24	instantiation	56, 32, 38	⊢
	: , : , :
25	instantiation	56, 32, 33	⊢
	: , : , :
26	instantiation	34	⊢
	:
27	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
29	instantiation	56, 35, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	instantiation	37, 38	⊢
	:
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	56, 40, 39	⊢
	: , : , :
34	axiom		⊢
	proveit.logic.equality.equals_reflexivity
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
36	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
37	theorem		⊢
	proveit.numbers.negation.real_closure
38	instantiation	56, 40, 41	⊢
	: , : , :
39	instantiation	56, 43, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	56, 43, 44	⊢
	: , : , :
42	instantiation	56, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
45	instantiation	47, 48, 53	⊢
	: , :
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
48	instantiation	49, 50, 51	⊢
	: , :
49	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
50	instantiation	52, 53	⊢
	:
51	instantiation	56, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.negation.int_closure
53	instantiation	56, 57, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
58	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements