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