Nuprl Lemma : consistent-context-model_wf
∀[Gamma:mFOL() List]. ∀[M:mfol-context-model()].  (consistent-context-model(Gamma;M) ∈ ℙ)
Proof
Definitions occuring in Statement : 
consistent-context-model: consistent-context-model(Gamma;M)
, 
mfol-context-model: mfol-context-model()
, 
mFOL: mFOL()
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
consistent-context-model: consistent-context-model(Gamma;M)
, 
mfol-context-model: mfol-context-model()
, 
prop: ℙ
, 
and: P ∧ Q
, 
so_lambda: λ2x.t[x]
, 
all: ∀x:A. B[x]
, 
so_apply: x[s]
Lemmas referenced : 
l_all_wf2, 
nat_wf, 
l_member_wf, 
consistent-model-const_wf, 
list_wf, 
consistent-model-fun_wf, 
mfol-context-model_wf, 
mFOL_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
productElimination, 
thin, 
productEquality, 
lemma_by_obid, 
isectElimination, 
hypothesis, 
atomEquality, 
because_Cache, 
hypothesisEquality, 
lambdaEquality, 
lambdaFormation, 
setElimination, 
rename, 
independent_pairEquality, 
setEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality
Latex:
\mforall{}[Gamma:mFOL()  List].  \mforall{}[M:mfol-context-model()].    (consistent-context-model(Gamma;M)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-10_32_20
Last ObjectModification:
2015_12_27-PM-06_24_25
Theory : minimal-first-order-logic
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