Nuprl Lemma : spread-axiom-sqequal-bottom
∀[F:Top]. (let a,b = Ax in F[a;b] ~ ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
spread: spread def,
sqequal: s ~ t,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2]
Lemmas referenced :
top_wf,
base_wf,
subtype_rel_self,
subtype_base_sq,
stuck-spread
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
lambdaFormation,
instantiate,
because_Cache,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[F:Top]. (let a,b = Ax in F[a;b] \msim{} \mbot{})
Date html generated:
2016_05_13-PM-03_45_01
Last ObjectModification:
2016_01_14-PM-07_06_17
Theory : computation
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