Nuprl Lemma : dl-prop-obj_wf
∀x:Prop. (prop(x) ∈ dl-Obj())
Proof
Definitions occuring in Statement :
dl-prop-obj: prop(x),
dl-prop: Prop,
dl-Obj: dl-Obj(),
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
dl-Obj: dl-Obj(),
dl-prop-obj: prop(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
dl-prop: Prop,
subtype_rel: A ⊆r B
Lemmas referenced :
mobj-ext,
dl-Spec_wf,
mrec_wf,
dl-prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
productElimination,
dependent_pairEquality_alt,
tokenEquality,
hypothesisEquality,
universeIsType,
applyEquality
Latex:
\mforall{}x:Prop. (prop(x) \mmember{} dl-Obj())
Date html generated:
2019_10_15-AM-11_39_15
Last ObjectModification:
2019_03_26-AM-11_24_02
Theory : dynamic!logic
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