Nuprl Lemma : K-dom_subtype
∀[K:mKripkeStruct]. ∀[i,j:World]. Dom(i) ⊆r Dom(j) supposing i ≤ j
Proof
Definitions occuring in Statement :
K-dom: Dom(i),
K-le: i ≤ j,
K-world: World,
mFO-Kripke-struct: mKripkeStruct,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
mFO-Kripke-struct: mKripkeStruct,
spreadn: spread4,
K-dom: Dom(i),
pi1: fst(t),
pi2: snd(t),
K-le: i ≤ j,
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T},
K-world: World,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
K-le_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
axiomEquality,
hypothesis,
universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
because_Cache,
applyEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[K:mKripkeStruct]. \mforall{}[i,j:World]. Dom(i) \msubseteq{}r Dom(j) supposing i \mleq{} j
Date html generated:
2019_10_16-AM-11_44_34
Last ObjectModification:
2018_10_13-AM-11_59_17
Theory : minimal-first-order-logic
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