Nuprl Lemma : mrec-ind_wf
∀[L:MutualRectypeSpec]. ∀[A:mobj(L) ⟶ TYPE]. ∀[h:x:mobj(L) ⟶ (z:{z:mobj(L)| z < x} ⟶ A[z]) ⟶ A[x]]. ∀[o:mobj(L)].
(mrec-ind(h;o) ∈ A[o])
Proof
Definitions occuring in Statement :
mrec-ind: mrec-ind(h;o),
mrec-lt: x < y,
mobj: mobj(L),
mrec_spec: MutualRectypeSpec,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mrec-ind: mrec-ind(h;o),
mrec-induction,
mobj-ext,
prec-induction-ext,
implies: P ⇒ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
mrec-induction,
mobj_wf,
mrec-lt_wf,
mrec_spec_wf,
mobj-ext,
prec-induction-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
thin,
instantiate,
extract_by_obid,
hypothesis,
applyEquality,
Error :lambdaEquality_alt,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
Error :isectIsType,
Error :functionIsType,
Error :universeIsType,
Error :TYPEIsType,
because_Cache,
Error :setIsType,
Error :TYPEMemberIsType,
setElimination,
rename,
axiomEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies
Latex:
\mforall{}[L:MutualRectypeSpec]. \mforall{}[A:mobj(L) {}\mrightarrow{} TYPE]. \mforall{}[h:x:mobj(L) {}\mrightarrow{} (z:\{z:mobj(L)| z < x\} {}\mrightarrow{} A[z]) {}\mrightarrow{} A[\000Cx]].
\mforall{}[o:mobj(L)].
(mrec-ind(h;o) \mmember{} A[o])
Date html generated:
2019_06_20-PM-02_16_27
Last ObjectModification:
2019_03_12-PM-11_33_36
Theory : tuples
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