Nuprl Lemma : mrec-lt_wf
∀[L:MutualRectypeSpec]. ∀[x,y:mobj(L)]. (x < y ∈ ℙ)
Proof
Definitions occuring in Statement :
mrec-lt: x < y,
mobj: mobj(L),
mrec_spec: MutualRectypeSpec,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mrec-lt: x < y,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
mrec: mrec(L;i),
subtype_rel: A ⊆r B,
mobj: mobj(L),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
mkinds: mKinds,
all: ∀x:A. B[x]
Lemmas referenced :
mobj_wf,
mrec_spec_wf,
prec_sub+_wf,
mrec-spec_wf,
istype-atom,
subtype_rel_product,
mkinds_wf,
mtype_wf,
mrec_wf,
subtype_rel-equal,
mtype-sqequal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
applyEquality,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
hypothesisEquality,
Error :isect_memberEquality_alt,
isectElimination,
thin,
Error :isectIsTypeImplies,
Error :universeIsType,
extract_by_obid,
atomEquality,
Error :lambdaEquality_alt,
independent_isectElimination,
setElimination,
rename,
because_Cache,
Error :lambdaFormation_alt
Latex:
\mforall{}[L:MutualRectypeSpec]. \mforall{}[x,y:mobj(L)]. (x < y \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_15_44
Last ObjectModification:
2019_02_25-PM-02_27_37
Theory : tuples
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