Nuprl Lemma : strong-subtype_functionality
∀[A1,B1,A2,B2:Type]. (A1 ≡ A2 ⇒ B1 ≡ B2 ⇒ strong-subtype(A1;B1) ⇒ strong-subtype(A2;B2))
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
strong-subtype: strong-subtype(A;B),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
cand: A c∧ B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
ext-eq_inversion,
subtype_rel_transitivity,
subtype_rel_weakening,
subtype_rel_wf,
exists_wf,
equal_wf,
ext-eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
because_Cache,
independent_pairFormation,
productEquality,
setEquality,
lambdaEquality,
applyEquality,
dependent_functionElimination,
independent_pairEquality,
axiomEquality,
universeEquality,
isect_memberEquality,
equalityElimination,
setElimination,
rename,
dependent_set_memberEquality,
dependent_pairFormation
Latex:
\mforall{}[A1,B1,A2,B2:Type]. (A1 \mequiv{} A2 {}\mRightarrow{} B1 \mequiv{} B2 {}\mRightarrow{} strong-subtype(A1;B1) {}\mRightarrow{} strong-subtype(A2;B2))
Date html generated:
2016_05_13-PM-04_11_07
Last ObjectModification:
2015_12_26-AM-11_21_52
Theory : subtype_1
Home
Index