Nuprl Lemma : subtype_rel-deq
∀[A,B:Type]. (EqDecider(B) ⊆r EqDecider(A)) supposing ((∀x,y:A. ((x = y ∈ B) ⇒ (x = y ∈ A))) and (A ⊆r B))
Proof
Definitions occuring in Statement :
deq: EqDecider(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Lemmas referenced :
subtype-deq
Rules used in proof :
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}[A,B:Type].
(EqDecider(B) \msubseteq{}r EqDecider(A)) supposing ((\mforall{}x,y:A. ((x = y) {}\mRightarrow{} (x = y))) and (A \msubseteq{}r B))
Date html generated:
2019_06_20-PM-00_32_05
Last ObjectModification:
2018_09_17-PM-05_40_26
Theory : equality!deciders
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