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	modus ponens	1, 2	⊢
1	instantiation	3, 4	⊢
	: , : , : , : , : , :
2	generalization	5	⊢
3	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
5	instantiation	8, 6	⊢
	: , : , :
6	instantiation	8, 7	⊢
	: , : , :
7	instantiation	8, 9	⊢
	: , : , :
8	axiom		⊢
	proveit.logic.equality.substitution
9	instantiation	10, 11, 12	⊢
	: , : , :
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	13, 14, 15, 40, 16, 17, 20, 24, 18	⊢
	: , : , : , : , : , :
12	instantiation	19, 24, 20, 21	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.disassociation
14	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
16	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
17	instantiation	22	⊢
	: , :
18	instantiation	23, 24	⊢
	:
19	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
20	instantiation	38, 27, 25	⊢
	: , : , :
21	instantiation	26	⊢
	:
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23	theorem		⊢
	proveit.numbers.negation.complex_closure
24	instantiation	38, 27, 28	⊢
	: , : , :
25	instantiation	29, 30, 31	⊢
	: , : , :
26	axiom		⊢
	proveit.logic.equality.equals_reflexivity
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	instantiation	38, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
30	instantiation	34, 35	⊢
	: , :
31	assumption		⊢
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
33	instantiation	38, 36, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
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.nat1