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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	5, 6, 25	⊢
	: , :
3	instantiation	7, 42, 8, 9, 10	⊢
	: , : , : , :
4	instantiation	19, 20, 45, 22, 11, 25, 12^*	⊢
	: , : , : , : , : , :
5	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_expansion
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
7	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
8	instantiation	13, 42	⊢
	: , :
9	instantiation	14	⊢
	: , : , : , :
10	instantiation	15	⊢
	:
11	instantiation	27	⊢
	: , :
12	instantiation	31, 16, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
15	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_4_repeats
16	instantiation	37, 18	⊢
	: , : , :
17	instantiation	19, 20, 45, 21, 22, 23, 24, 25, 26^*	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
19	theorem		⊢
	proveit.numbers.multiplication.association
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	instantiation	27	⊢
	: , :
24	instantiation	43, 29, 28	⊢
	: , : , :
25	instantiation	43, 29, 30	⊢
	: , : , :
26	instantiation	31, 32, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	43, 35, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	43, 35, 36	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	37, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
34	instantiation	43, 40, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	43, 40, 41	⊢
	: , : , :
37	axiom		⊢
	proveit.logic.equality.substitution
38	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
39	instantiation	43, 44, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	43, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements