Nuprl Lemma : pertype_wf
∀[R:Base ⟶ Base ⟶ ℙ]
(pertype(R) ∈ Type) supposing ((∀x,y:Base. (R[x;y] ⇒ R[y;x])) and (∀x,y,z:Base. (R[x;y] ⇒ R[y;z] ⇒ R[x;z])))
Proof
Definitions occuring in Statement :
pertype: pertype(R),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
function: x:A ⟶ B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
so_apply: x[s],
subtype_rel: A ⊆r B,
guard: {T},
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
base_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
lambdaEquality,
functionEquality,
applyEquality,
hypothesisEquality,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality,
instantiate,
pertypeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[R:Base {}\mrightarrow{} Base {}\mrightarrow{} \mBbbP{}]
(pertype(R) \mmember{} Type) supposing
((\mforall{}x,y:Base. (R[x;y] {}\mRightarrow{} R[y;x])) and
(\mforall{}x,y,z:Base. (R[x;y] {}\mRightarrow{} R[y;z] {}\mRightarrow{} R[x;z])))
Date html generated:
2019_06_20-AM-11_29_51
Last ObjectModification:
2018_08_07-PM-02_29_01
Theory : per!type!1
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