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	reference	29	⊢
2	instantiation	34, 4	⊢
	: , : , :
3	instantiation	5, 6, 7, 8	⊢
	: , : , : , :
4	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
5	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
6	instantiation	9, 10, 20	⊢
	: , :
7	instantiation	11, 23, 12, 13, 14	⊢
	: , : , : , :
8	instantiation	15, 16, 40, 17, 18, 19, 20, 21^*	⊢
	: , : , : , : , : , :
9	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_expansion
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
11	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
12	instantiation	22, 23	⊢
	: , :
13	instantiation	24	⊢
	: , : , :
14	instantiation	25	⊢
	:
15	theorem		⊢
	proveit.numbers.multiplication.association
16	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
18	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19	instantiation	26	⊢
	: , :
20	instantiation	38, 27, 28	⊢
	: , : , :
21	instantiation	29, 30, 31	⊢
	: , : , :
22	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
25	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_3_repeats
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	instantiation	38, 32, 33	⊢
	: , : , :
29	axiom		⊢
	proveit.logic.equality.equals_transitivity
30	instantiation	34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
33	instantiation	38, 36, 37	⊢
	: , : , :
34	axiom		⊢
	proveit.logic.equality.substitution
35	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	38, 39, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements