Nuprl Lemma : K_uforces_quant_lemma
∀body,z,isall,K:Top.
  (K-uforces(K;mFOquant(isall;z;body)) ~ if isall
  then λi,a. ∀[j:World]. ∀v:Dom(j). (K-uforces(K;body) j a[z := v]) supposing i ≤ j
  else λi,a. ∃v:Dom(i). (K-uforces(K;body) i a[z := v])
  fi )
Proof
Definitions occuring in Statement : 
K-uforces: K-uforces(K;fmla)
, 
K-dom: Dom(i)
, 
K-le: i ≤ j
, 
K-world: World
, 
mFOquant: mFOquant(isall;var;body)
, 
update-assignment: a[x := v]
, 
ifthenelse: if b then t else f fi 
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
apply: f a
, 
lambda: λx.A[x]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
K-uforces: K-uforces(K;fmla)
, 
mFOquant: mFOquant(isall;var;body)
, 
mFOL_ind: mFOL_ind, 
member: t ∈ T
Lemmas referenced : 
istype-top
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
cut, 
sqequalRule, 
hypothesis, 
inhabitedIsType, 
hypothesisEquality, 
introduction, 
extract_by_obid
Latex:
\mforall{}body,z,isall,K:Top.
    (K-uforces(K;mFOquant(isall;z;body))  \msim{}  if  isall
    then  \mlambda{}i,a.  \mforall{}[j:World].  \mforall{}v:Dom(j).  (K-uforces(K;body)  j  a[z  :=  v])  supposing  i  \mleq{}  j
    else  \mlambda{}i,a.  \mexists{}v:Dom(i).  (K-uforces(K;body)  i  a[z  :=  v])
    fi  )
Date html generated:
2019_10_16-AM-11_45_37
Last ObjectModification:
2018_10_16-AM-10_52_49
Theory : minimal-first-order-logic
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