Nuprl Lemma : as_strong_transitivity
∀[T:Type]. ∀[P,Q,R:T ⟶ ℙ]. (P as strong as Q ⇒ Q as strong as R ⇒ P as strong as R )
Proof
Definitions occuring in Statement :
as_strong: P as strong as Q ,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
as_strong: P as strong as Q ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
applyEquality,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
functionEquality,
hypothesis,
Error :inhabitedIsType,
Error :functionIsType,
Error :universeIsType,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[P,Q,R:T {}\mrightarrow{} \mBbbP{}]. (P as strong as Q {}\mRightarrow{} Q as strong as R {}\mRightarrow{} P as strong as R )
Date html generated:
2019_06_20-PM-00_31_37
Last ObjectModification:
2018_09_26-AM-11_46_30
Theory : relations
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