Nuprl Lemma : dl-prop-atoms_wf
dl-prop-atoms() ∈ ∀x:dl-Obj(). (ℕ List)
Proof
Definitions occuring in Statement :
dl-prop-atoms: dl-prop-atoms(),
dl-Obj: dl-Obj(),
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
dl-prop-atoms: dl-prop-atoms(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
dl-ind_wf,
list_wf,
nat_wf,
subtype-TYPE,
dl-Obj_wf,
nil_wf,
istype-nat,
append_wf,
dl-prog_wf,
dl-prop_wf,
cons_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality_alt,
hypothesis,
applyEquality,
universeIsType,
hypothesisEquality,
inhabitedIsType,
because_Cache
Latex:
dl-prop-atoms() \mmember{} \mforall{}x:dl-Obj(). (\mBbbN{} List)
Date html generated:
2019_10_15-AM-11_43_53
Last ObjectModification:
2019_03_26-AM-11_30_55
Theory : dynamic!logic
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