Nuprl Lemma : dl-valid_wf
∀[phi:Prop]. (|= phi ∈ ℙ')
Proof
Definitions occuring in Statement :
dl-valid: |= phi,
dl-prop: Prop,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dl-valid: |= phi,
prop: ℙ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
nat_wf,
dl-prop-sem_wf,
istype-nat,
subtype_rel_self,
dl-prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
universeEquality,
cumulativity,
extract_by_obid,
hypothesis,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality_alt,
instantiate,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[phi:Prop]. (|= phi \mmember{} \mBbbP{}')
Date html generated:
2019_10_15-AM-11_44_11
Last ObjectModification:
2019_03_27-AM-00_13_57
Theory : dynamic!logic
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