Nuprl Lemma : do-apply_wf
∀[A,B:Type]. ∀[f:A ⟶ (B + Top)]. ∀[x:A]. do-apply(f;x) ∈ B supposing ↑can-apply(f;x)
Proof
Definitions occuring in Statement :
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
outl_wf,
top_wf,
assert_wf,
isl_wf,
can-apply_wf,
subtype_rel_dep_function,
subtype_rel_union
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
independent_isectElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
axiomEquality,
lambdaEquality,
unionEquality,
because_Cache,
isect_memberEquality,
voidElimination,
voidEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} (B + Top)]. \mforall{}[x:A]. do-apply(f;x) \mmember{} B supposing \muparrow{}can-apply(f;x)
Date html generated:
2016_05_15-PM-03_28_45
Last ObjectModification:
2015_12_27-PM-01_09_35
Theory : general
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