Nuprl Lemma : dlo-le_wf
dlo-le() ∈ dl-Obj() ⟶ dl-Obj() ⟶ 𝔹
Proof
Definitions occuring in Statement :
dlo-le: dlo-le(),
dl-Obj: dl-Obj(),
bool: 𝔹,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
dlo-le: dlo-le(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
all: ∀x:A. B[x],
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,
dl-Obj_wf,
bool_wf,
subtype-TYPE,
dlo_eq_wf,
dl-prog-obj_wf,
dl-aprog_wf,
istype-nat,
bor_wf,
dl-comp_wf,
dl-prog_wf,
dl-choose_wf,
dl-iterate_wf,
dl-test_wf,
dl-prop_wf,
dl-prop-obj_wf,
dl-aprop_wf,
dl-false_wf,
dl-implies_wf,
dl-and_wf,
dl-or_wf,
dl-box_wf,
dl-diamond_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality_alt,
functionEquality,
hypothesis,
applyEquality,
universeIsType,
dependent_functionElimination,
hypothesisEquality,
inhabitedIsType,
functionIsType
Latex:
dlo-le() \mmember{} dl-Obj() {}\mrightarrow{} dl-Obj() {}\mrightarrow{} \mBbbB{}
Date html generated:
2019_10_15-AM-11_43_13
Last ObjectModification:
2019_04_11-PM-01_53_48
Theory : dynamic!logic
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