Nuprl Lemma : family-monotone_wf
∀[P:Type]. ∀[H:(P ⟶ Type) ⟶ P ⟶ Type]. (family-monotone{i:l}(P;H) ∈ ℙ')
Proof
Definitions occuring in Statement :
family-monotone: family-monotone{i:l}(P;H),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
family-monotone: family-monotone{i:l}(P;H),
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
all_wf,
sub-family_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[P:Type]. \mforall{}[H:(P {}\mrightarrow{} Type) {}\mrightarrow{} P {}\mrightarrow{} Type]. (family-monotone\{i:l\}(P;H) \mmember{} \mBbbP{}')
Date html generated:
2016_05_14-AM-06_12_15
Last ObjectModification:
2015_12_26-PM-00_06_12
Theory : co-recursion
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