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