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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