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, 5	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
2	instantiation	41, 6, 7	⊢
	: , : , :
3	instantiation	8, 9, 10	⊢
	: , :
4	reference	9	⊢
5	instantiation	11, 33, 19, 30, 12, 13, 14^*	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
7	instantiation	41, 15, 40	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
9	instantiation	41, 16, 17	⊢
	: , : , :
10	instantiation	18, 19, 20	⊢
	:
11	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
12	instantiation	21, 29, 30, 31	⊢
	: , : , :
13	instantiation	22, 43	⊢
	:
14	instantiation	23, 24	⊢
	:
15	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
17	instantiation	41, 25, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
19	instantiation	27, 29, 30, 31	⊢
	: , : , :
20	instantiation	28, 29, 30, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
23	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
24	instantiation	41, 32, 33	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
30	instantiation	41, 35, 34	⊢
	: , : , :
31	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	41, 35, 36	⊢
	: , : , :
34	instantiation	41, 38, 37	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	41, 38, 39	⊢
	: , : , :
37	instantiation	41, 42, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	41, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
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.nat2
^*equality replacement requirements