Nuprl Lemma : non-void-decl-join
∀[T:Type]. ∀eq:EqDecider(T). ∀d1,d2:a:T fp-> Type. (non-void(d1) ⇒ non-void(d2) ⇒ non-void(d1 ⊕ d2))
Proof
Definitions occuring in Statement :
non-void-decl: non-void(d),
fpf-join: f ⊕ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
non-void-decl: non-void(d),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top
Lemmas referenced :
fpf-all-join-decl,
istype-universe,
fpf-all_wf,
subtype_rel_universe1,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
istype-void,
fpf_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
lambdaEquality_alt,
inhabitedIsType,
hypothesis,
independent_functionElimination,
universeIsType,
instantiate,
cumulativity,
universeEquality,
applyEquality,
setIsType,
because_Cache,
independent_isectElimination,
isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}[T:Type]
\mforall{}eq:EqDecider(T). \mforall{}d1,d2:a:T fp-> Type. (non-void(d1) {}\mRightarrow{} non-void(d2) {}\mRightarrow{} non-void(d1 \moplus{} d2))
Date html generated:
2019_10_16-AM-11_26_23
Last ObjectModification:
2018_10_10-PM-02_05_12
Theory : finite!partial!functions
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