Nuprl Lemma : fun-ss_wf
∀[ss:SeparationSpace]. ∀[A:Type]. (A ⟶ ss ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
fun-ss: A ⟶ ss,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fun-ss: A ⟶ ss,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
fun-sep: fun-sep(ss;A;f;g),
exists: ∃x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
separation-space: SeparationSpace,
record+: record+,
record-select: r.x,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
ss-sep: x # y,
ss-point: Point(ss)
Lemmas referenced :
mk-ss_wf,
ss-point_wf,
fun-sep_wf,
ss-sep-irrefl,
istype-void,
subtype_rel_self,
ss-sep_wf,
record-select_wf,
top_wf,
istype-atom,
not_wf,
all_wf,
or_wf,
istype-universe,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
inhabitedIsType,
functionIsType,
universeIsType,
lambdaFormation_alt,
productElimination,
applyEquality,
independent_functionElimination,
voidElimination,
because_Cache,
spreadEquality,
productEquality,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
tokenEquality,
instantiate,
universeEquality,
setEquality,
cumulativity,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
unionElimination,
inlEquality_alt,
dependent_pairEquality_alt,
inrEquality_alt,
equalityIstype,
dependent_functionElimination,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[ss:SeparationSpace]. \mforall{}[A:Type]. (A {}\mrightarrow{} ss \mmember{} SeparationSpace)
Date html generated:
2019_10_31-AM-07_26_41
Last ObjectModification:
2019_09_19-PM-04_08_53
Theory : constructive!algebra
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