Nuprl Lemma : mrec_ind_wf
∀L:MutualRectypeSpec. ∀[P:mobj(L) ⟶ TYPE]. ∀[h:mrecind(L;x.P[x])]. ∀[x:mobj(L)]. (mrec_ind(L;h;x) ∈ P[x])
Proof
Definitions occuring in Statement :
mrec_ind: mrec_ind(L;h;x),
mrecind: mrecind(L;x.P[x]),
mobj: mobj(L),
mrec_spec: MutualRectypeSpec,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
mrec_ind: mrec_ind(L;h;x),
mrec-induction2-ext,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
mrec-induction2-ext,
mobj_wf,
istype-mrecind,
mrec_spec_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
applyEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
because_Cache,
sqequalHypSubstitution,
Error :inhabitedIsType,
independent_functionElimination,
hypothesisEquality,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
Error :universeIsType,
isectElimination,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :lambdaEquality_alt,
Error :functionIsType,
Error :TYPEIsType
Latex:
\mforall{}L:MutualRectypeSpec
\mforall{}[P:mobj(L) {}\mrightarrow{} TYPE]. \mforall{}[h:mrecind(L;x.P[x])]. \mforall{}[x:mobj(L)]. (mrec\_ind(L;h;x) \mmember{} P[x])
Date html generated:
2019_06_20-PM-02_16_23
Last ObjectModification:
2019_03_12-PM-11_32_21
Theory : tuples
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