Nuprl Lemma : strong-subtype_witness
∀[A,B:Type]. (strong-subtype(A;B) ⇒ (<Ax, Ax> ∈ strong-subtype(A;B)))
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
pair: <a, b>,
universe: Type,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
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
Lemmas referenced :
exists_wf,
equal_wf,
strong-subtype_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
independent_pairEquality,
axiomEquality,
lambdaEquality,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
hypothesis,
productElimination,
thin,
setEquality,
lemma_by_obid,
isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. (strong-subtype(A;B) {}\mRightarrow{} (<Ax, Ax> \mmember{} strong-subtype(A;B)))
Date html generated:
2016_05_13-PM-04_10_57
Last ObjectModification:
2015_12_26-AM-11_21_43
Theory : subtype_1
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