Nuprl Lemma : corec-family-wf2
∀[P:𝕌{j}]. ∀[H:(P ⟶ Type) ⟶ P ⟶ Type]. (corec-family(H) ∈ P ⟶ Type)
Proof
Definitions occuring in Statement :
corec-family: corec-family(H),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
corec-family: corec-family(H),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
isect-family-wf2,
nat_wf,
fun_exp_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
lemma_by_obid,
lambdaEquality,
applyEquality,
instantiate
Latex:
\mforall{}[P:\mBbbU{}\{j\}]. \mforall{}[H:(P {}\mrightarrow{} Type) {}\mrightarrow{} P {}\mrightarrow{} Type]. (corec-family(H) \mmember{} P {}\mrightarrow{} Type)
Date html generated:
2016_05_14-AM-06_12_20
Last ObjectModification:
2015_12_26-PM-00_06_08
Theory : co-recursion
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