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	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	4, 18, 5, 47, 19, 6, 22, 12, 7^*	⊢
	: , : , : , : , : , :
3	instantiation	17, 18, 44, 19, 8, 22, 9^*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
6	instantiation	10	⊢
	: , : , : , :
7	instantiation	11, 12	⊢
	:
8	instantiation	27	⊢
	: , :
9	instantiation	31, 13, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
11	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
12	instantiation	45, 29, 15	⊢
	: , : , :
13	instantiation	39, 16	⊢
	: , : , :
14	instantiation	17, 18, 44, 47, 19, 20, 21, 22, 23^*	⊢
	: , : , : , : , : , :
15	instantiation	24, 25, 26	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
17	theorem		⊢
	proveit.numbers.addition.association
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	27	⊢
	: , :
21	instantiation	45, 29, 28	⊢
	: , : , :
22	instantiation	45, 29, 30	⊢
	: , : , :
23	instantiation	31, 32, 33	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
25	instantiation	34, 35	⊢
	: , :
26	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	45, 37, 36	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	45, 37, 38	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	39, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
34	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
36	instantiation	45, 42, 41	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	45, 42, 43	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.substitution
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
41	instantiation	45, 46, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	45, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements