Nuprl Lemma : strong-subtype-l_member-type
∀[A,B:Type]. ∀[L:A List]. ∀[x:B]. x ∈ A supposing (x ∈ L) supposing strong-subtype(A;B)
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
list: T List,
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
l_member: (x ∈ l),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q
Lemmas referenced :
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
select_wf,
equal_wf,
exists_wf,
strong-subtype_wf,
list_wf,
subtype_rel_list,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
applyEquality,
hypothesis,
sqequalRule,
lemma_by_obid,
isectElimination,
hypothesisEquality,
because_Cache,
independent_isectElimination,
universeEquality,
dependent_set_memberEquality,
lambdaEquality,
dependent_pairFormation,
cumulativity,
setElimination,
rename,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[A,B:Type]. \mforall{}[L:A List]. \mforall{}[x:B]. x \mmember{} A supposing (x \mmember{} L) supposing strong-subtype(A;B)
Date html generated:
2016_05_14-AM-07_40_37
Last ObjectModification:
2016_01_15-AM-08_35_59
Theory : list_1
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