Nuprl Lemma : mFO-Kripke-struct_wf
mKripkeStruct ∈ 𝕌'
Proof
Definitions occuring in Statement :
mFO-Kripke-struct: mKripkeStruct,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
mFO-Kripke-struct: mKripkeStruct,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
spreadn: spread4,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
and: P ∧ Q,
FOStruct: FOStruct(Dom),
uimplies: b supposing a,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
FOStruct_wf,
all_wf,
subtype_rel_self,
subtype_rel_wf,
list_wf,
subtype_rel_list,
istype-atom
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
setEquality,
productEquality,
closedConclusion,
universeEquality,
functionEquality,
cumulativity,
hypothesisEquality,
because_Cache,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesis,
productElimination,
lambdaEquality_alt,
instantiate,
atomEquality,
independent_isectElimination,
universeIsType,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry
Latex:
mKripkeStruct \mmember{} \mBbbU{}'
Date html generated:
2019_10_16-AM-11_43_55
Last ObjectModification:
2018_10_12-PM-09_52_47
Theory : minimal-first-order-logic
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