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	reference	10	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 9^*	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	10, 11, 12	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
7	instantiation	53, 13, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
9	instantiation	15, 16	⊢
	:
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	17, 18, 48, 55, 19, 20, 23, 24, 21	⊢
	: , : , : , : , : , :
12	instantiation	22, 23, 24, 25	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
14	instantiation	53, 26, 27	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
16	instantiation	53, 31, 28	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.disassociation
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	29	⊢
	: , :
21	instantiation	53, 31, 30	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
23	instantiation	53, 31, 37	⊢
	: , : , :
24	instantiation	53, 31, 32	⊢
	: , : , :
25	instantiation	33	⊢
	:
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27	instantiation	53, 34, 35	⊢
	: , : , :
28	instantiation	53, 46, 36	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30	instantiation	38, 37	⊢
	:
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	38, 39	⊢
	:
33	axiom		⊢
	proveit.logic.equality.equals_reflexivity
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
35	instantiation	53, 40, 41	⊢
	: , : , :
36	instantiation	53, 51, 42	⊢
	: , : , :
37	instantiation	43, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.negation.real_closure
39	instantiation	53, 46, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
42	instantiation	53, 54, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
44	instantiation	49, 50	⊢
	: , :
45	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
47	instantiation	53, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
49	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	53, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements