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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