Nuprl Lemma : strong-subtype-discrete-type
∀[A,B:Type]. (discrete-type(A)) supposing (discrete-type(B) and strong-subtype(A;B))
Proof
Definitions occuring in Statement :
discrete-type: discrete-type(T),
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,
discrete-type: discrete-type(T),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
guard: {T}
Lemmas referenced :
req_wf,
real_wf,
all_wf,
equal_wf,
discrete-type_wf,
strong-subtype_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
functionExtensionality,
applyEquality,
hypothesisEquality,
productElimination,
sqequalRule,
because_Cache,
independent_functionElimination,
extract_by_obid,
isectElimination,
lambdaEquality,
functionEquality,
cumulativity,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_set_memberEquality,
dependent_pairFormation
Latex:
\mforall{}[A,B:Type]. (discrete-type(A)) supposing (discrete-type(B) and strong-subtype(A;B))
Date html generated:
2018_05_22-PM-02_13_27
Last ObjectModification:
2017_10_30-AM-00_37_14
Theory : reals
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