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