Nuprl Lemma : can-apply_wf
∀[A:Type]. ∀[f:A ⟶ (Top + Top)]. ∀[x:A]. (can-apply(f;x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
can-apply: can-apply(f;x),
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
can-apply: can-apply(f;x),
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
isl_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
unionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} (Top + Top)]. \mforall{}[x:A]. (can-apply(f;x) \mmember{} \mBbbB{})
Date html generated:
2016_05_15-PM-03_28_39
Last ObjectModification:
2015_12_27-PM-01_09_17
Theory : general
Home
Index