Nuprl Lemma : stable__ss-function
∀[X,Y:SeparationSpace]. ∀[f:Point(X) ⟶ Point(Y)]. Stable{ss-function(X;Y;f)}
Proof
Definitions occuring in Statement :
ss-function: ss-function(X;Y;f),
ss-point: Point(ss),
separation-space: SeparationSpace,
stable: Stable{P},
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
false: False,
not: ¬A,
ss-eq: x ≡ y,
uimplies: b supposing a,
stable: Stable{P},
all: ∀x:A. B[x],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
ss-function: ss-function(X;Y;f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
ss-function_wf,
not_wf,
ss-sep_wf,
stable__ss-eq,
stable__implies,
ss-eq_wf,
all_wf,
ss-point_wf,
stable__all
Rules used in proof :
voidElimination,
equalitySymmetry,
equalityTransitivity,
dependent_functionElimination,
isect_memberEquality,
because_Cache,
lambdaFormation,
independent_functionElimination,
applyEquality,
functionEquality,
lambdaEquality,
sqequalRule,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y:SeparationSpace]. \mforall{}[f:Point(X) {}\mrightarrow{} Point(Y)]. Stable\{ss-function(X;Y;f)\}
Date html generated:
2018_07_29-AM-10_10_53
Last ObjectModification:
2018_07_03-PM-04_49_49
Theory : constructive!algebra
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