Nuprl Lemma : implies-mrec-lt
∀[L:MutualRectypeSpec]. ∀[x:mobj(L)]. ∀y:mobj(L). ((prec_sub(Atom;lbl,p.mrec-spec(L;lbl;p)) x y) ⇒ x < y)
Proof
Definitions occuring in Statement :
mrec-lt: x < y,
mobj: mobj(L),
mrec-spec: mrec-spec(L;lbl;p),
mrec_spec: MutualRectypeSpec,
prec_sub: prec_sub(P;lbl,p.a[lbl; p]),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
mrec: mrec(L;i),
mrec-lt: x < y,
prec_sub+: prec_sub+(P;lbl,p.a[lbl; p]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
mobj: mobj(L),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
mobj-ext,
prec_sub_wf,
mrec-spec_wf,
istype-atom,
subtype_rel_self,
mobj_wf,
subtype_rel_transitivity,
mkinds_wf,
mtype_wf,
prec_wf,
mrec_spec_wf,
implies-rel_plus
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
sqequalRule,
Error :lambdaFormation_alt,
Error :universeIsType,
applyEquality,
closedConclusion,
atomEquality,
Error :lambdaEquality_alt,
hypothesis,
Error :inhabitedIsType,
productEquality,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[L:MutualRectypeSpec]. \mforall{}[x:mobj(L)].
\mforall{}y:mobj(L). ((prec\_sub(Atom;lbl,p.mrec-spec(L;lbl;p)) x y) {}\mRightarrow{} x < y)
Date html generated:
2019_06_20-PM-02_15_49
Last ObjectModification:
2019_02_26-AM-11_59_44
Theory : tuples
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