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, 9^*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.addition.association
2	reference	49	⊢
3	reference	27	⊢
4	instantiation	28	⊢
	: , :
5	instantiation	47, 34, 10	⊢
	: , : , :
6	reference	31	⊢
7	instantiation	47, 34, 11	⊢
	: , : , :
8	reference	22	⊢
9	instantiation	12, 13, 14^*	⊢
	: , :
10	instantiation	17, 15, 16	⊢
	: , :
11	instantiation	17, 29, 35	⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.equals_reversal
13	instantiation	18, 19, 27, 49, 20, 21, 22, 23, 31, 24^*	⊢
	: , : , : , : , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_3
15	instantiation	47, 43, 25	⊢
	: , : , :
16	instantiation	26, 35, 27	⊢
	: , :
17	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
18	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
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	28	⊢
	: , :
22	instantiation	47, 34, 40	⊢
	: , : , :
23	instantiation	47, 34, 29	⊢
	: , : , :
24	instantiation	30, 31	⊢
	:
25	instantiation	47, 45, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	instantiation	47, 43, 33	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
31	instantiation	47, 34, 35	⊢
	: , : , :
32	instantiation	47, 48, 36	⊢
	: , : , :
33	instantiation	47, 45, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	38, 39, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
37	instantiation	47, 48, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
40	instantiation	47, 43, 44	⊢
	: , : , :
41	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	47, 45, 46	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	47, 48, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements