Nuprl Lemma : K_forces_quant_lemma
∀body,z,isall,K:Top.
  (K-forces(K;mFOquant(isall;z;body)) ~ if isall
  then λi,a. ∀j:{j:World| i ≤ j} . ∀v:Dom(j).  (K-forces(K;body) j a[z := v])
  else λi,a. ∃v:Dom(i). (K-forces(K;body) i a[z := v])
  fi )
Proof
Definitions occuring in Statement : 
K-forces: K-forces(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 
, 
top: Top
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
set: {x:A| B[x]} 
, 
apply: f a
, 
lambda: λx.A[x]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
K-forces: K-forces(K;fmla)
, 
mFOquant: mFOquant(isall;var;body)
, 
mFOL_ind: mFOL_ind, 
member: t ∈ T
Lemmas referenced : 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
cut, 
sqequalRule, 
hypothesis, 
inhabitedIsType, 
hypothesisEquality, 
universeIsType, 
introduction, 
extract_by_obid
Latex:
\mforall{}body,z,isall,K:Top.
    (K-forces(K;mFOquant(isall;z;body))  \msim{}  if  isall
    then  \mlambda{}i,a.  \mforall{}j:\{j:World|  i  \mleq{}  j\}  .  \mforall{}v:Dom(j).    (K-forces(K;body)  j  a[z  :=  v])
    else  \mlambda{}i,a.  \mexists{}v:Dom(i).  (K-forces(K;body)  i  a[z  :=  v])
    fi  )
Date html generated:
2019_10_16-AM-11_45_12
Last ObjectModification:
2018_10_15-PM-06_44_38
Theory : minimal-first-order-logic
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