Nuprl Lemma : record+_subtype_rel
∀[T:Type]. ∀[B:T ⟶ Type]. ∀[z:Atom]. (T; z:B[self] ⊆r T)
Proof
Definitions occuring in Statement :
record+: record+,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
record+: record+,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
dep-isect-subtype,
ifthenelse_wf,
eq_atom_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
atomEquality,
instantiate,
isectElimination,
hypothesis,
universeEquality,
applyEquality,
axiomEquality,
isect_memberEquality,
because_Cache,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[B:T {}\mrightarrow{} Type]. \mforall{}[z:Atom]. (T; z:B[self] \msubseteq{}r T)
Date html generated:
2016_05_15-PM-06_39_20
Last ObjectModification:
2015_12_27-AM-11_53_17
Theory : general
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