Nuprl Lemma : insert-no-combine-permutation
∀T:Type. ∀cmp:comparison(T). ∀L:T List. ∀u:T. permutation(T;insert-no-combine(cmp;u;L);[u] @ L)
Proof
Definitions occuring in Statement :
insert-no-combine: insert-no-combine(cmp;x;l),
comparison: comparison(T),
permutation: permutation(T;L1;L2),
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
insert-no-combine: insert-no-combine(cmp;x;l),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
append: as @ bs,
uimplies: b supposing a,
comparison: comparison(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
all_wf,
permutation_wf,
insert-no-combine_wf,
append_wf,
cons_wf,
nil_wf,
list_wf,
list_ind_nil_lemma,
list_ind_cons_lemma,
permutation_weakening,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
comparison_wf,
permutation_functionality_wrt_permutation,
cons_functionality_wrt_permutation,
permutation-swap-first2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
independent_isectElimination,
rename,
natural_numberEquality,
applyEquality,
setElimination,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}cmp:comparison(T). \mforall{}L:T List. \mforall{}u:T. permutation(T;insert-no-combine(cmp;u;L);[u] @ L)
Date html generated:
2017_04_17-AM-08_30_42
Last ObjectModification:
2017_02_27-PM-04_52_15
Theory : list_1
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