Nuprl Lemma : strong-subtype-list
∀[A,B:Type]. strong-subtype(A List;B List) supposing strong-subtype(A;B)
Proof
Definitions occuring in Statement :
list: T List,
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
guard: {T},
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
nil: [],
it: ⋅,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b)
Lemmas referenced :
strong-subtype-implies,
subtype_rel_list,
list_wf,
exists_wf,
equal_wf,
strong-subtype_witness,
strong-subtype_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
nil_wf,
equal-wf-base-T,
product_subtype_list,
spread_cons_lemma,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
null_nil_lemma,
btrue_wf,
null_cons_lemma,
bfalse_wf,
and_wf,
null_wf,
btrue_neq_bfalse,
subtype_rel_transitivity,
cons_wf,
reduce_hd_cons_lemma,
hd_wf,
squash_wf,
length_wf,
length_cons_ge_one,
top_wf,
reduce_tl_cons_lemma,
tl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
productElimination,
independent_isectElimination,
independent_pairFormation,
lambdaEquality,
setEquality,
cumulativity,
sqequalRule,
applyEquality,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
setElimination,
rename,
lambdaFormation,
intWeakElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
unionElimination,
baseClosed,
promote_hyp,
hypothesis_subsumption,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
instantiate,
imageElimination,
addLevel,
levelHypothesis,
imageMemberEquality
Latex:
\mforall{}[A,B:Type]. strong-subtype(A List;B List) supposing strong-subtype(A;B)
Date html generated:
2017_04_14-AM-09_27_20
Last ObjectModification:
2017_02_27-PM-04_01_16
Theory : list_1
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