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	axiom		⊢
	proveit.logic.equality.substitution
2	modus ponens	5, 6	, ⊢
3	instantiation	7, 35	⊢
	: , :
4	instantiation	7, 35	⊢
	: , :
5	instantiation	8, 9	⊢
	: , : , : , : , : , : , :
6	generalization	10	, ⊢
7	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
8	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
10	instantiation	11, 12, 40, 13, 14, 15, 16, 17, 18, 19	, , ⊢
	: , : , : , : , : , :
11	theorem		⊢
	proveit.numbers.multiplication.association
12	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	20	⊢
	: , :
15	instantiation	20	⊢
	: , :
16	instantiation	41, 23, 21	⊢
	: , : , :
17	instantiation	41, 23, 22	⊢
	: , : , :
18	instantiation	41, 23, 26	⊢
	: , : , :
19	instantiation	41, 23, 24	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	assumption		⊢
22	assumption		⊢
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	25, 26, 27	⊢
	: , :
25	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
26	instantiation	41, 29, 28	⊢
	: , : , :
27	instantiation	41, 29, 30	⊢
	: , : , :
28	instantiation	41, 32, 31	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
30	instantiation	41, 32, 33	⊢
	: , : , :
31	instantiation	41, 34, 35	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
33	instantiation	41, 42, 36	⊢
	: , : , :
34	instantiation	37, 38, 39	⊢
	: , :
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
37	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
38	instantiation	41, 42, 40	⊢
	: , : , :
39	instantiation	41, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements