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^	, ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
2	reference	10	⊢
3	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
4	instantiation	7, 42, 20, 22, 35, 8	⊢
	: , : , : , : , :
5	instantiation	9, 10	⊢
	:
6	instantiation	15, 11, 12	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
8	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
9	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
10	assumption		⊢
11	instantiation	13, 42, 21, 20, 14, 22, 24, 25	⊢
	: , : , : , : , : , :
12	instantiation	15, 16, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.disassociation
14	instantiation	27	⊢
	: , :
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	18, 42, 20, 22, 24, 25	⊢
	: , : , : , : , : , : , :
17	instantiation	19, 20, 21, 42, 22, 23, 24, 25, 26^*	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.addition.leftward_commutation
19	theorem		⊢
	proveit.numbers.addition.association
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	instantiation	27	⊢
	: , :
24	instantiation	40, 29, 28	⊢
	: , : , :
25	instantiation	40, 29, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	40, 31, 32	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	33, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
32	instantiation	40, 36, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
34	instantiation	38, 39	⊢
	: , :
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	40, 41, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements