Nuprl Lemma : param-W_wf
∀[P:Type]. ∀[A:P ⟶ Type]. ∀[B:p:P ⟶ A[p] ⟶ Type]. ∀[C:p:P ⟶ a:A[p] ⟶ B[p;a] ⟶ P]. (pW ∈ P ⟶ Type)
Proof
Definitions occuring in Statement :
param-W: pW,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
param-W: pW,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
implies: P ⇒ Q,
prop: ℙ,
pcw-path: Path,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
exists: ∃x:A. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
param-co-W_wf,
all_wf,
pcw-path_wf,
pcw-step-agree_wf,
false_wf,
le_wf,
squash_wf,
exists_wf,
nat_wf,
pcw-pp-barred_wf,
pcw-partial_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
setEquality,
applyEquality,
cumulativity,
because_Cache,
functionEquality,
setElimination,
rename,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
universeEquality
Latex:
\mforall{}[P:Type]. \mforall{}[A:P {}\mrightarrow{} Type]. \mforall{}[B:p:P {}\mrightarrow{} A[p] {}\mrightarrow{} Type]. \mforall{}[C:p:P {}\mrightarrow{} a:A[p] {}\mrightarrow{} B[p;a] {}\mrightarrow{} P].
(pW \mmember{} P {}\mrightarrow{} Type)
Date html generated:
2016_05_14-AM-06_13_17
Last ObjectModification:
2015_12_26-PM-00_05_38
Theory : co-recursion
Home
Index