Nuprl Lemma : DCC-order-type-less-ext
DCC(WFO{i:l}();order-type-less())
Proof
Definitions occuring in Statement :
WFO: WFO{i:l}(),
order-type-less: order-type-less(),
DCC: DCC(T;<)
Definitions unfolded in proof :
member: t ∈ T,
pi1: fst(t),
compose: f o g,
lt_int: i <z j,
btrue: tt,
it: ⋅,
bfalse: ff,
subtract: n - m,
genrec-ap: genrec-ap,
spreadn: spread4,
spreadn: spread3,
DCC-order-type: DCC-order-type(),
DCC-order-type-less,
any: any x,
bool_cases_sqequal,
complete-nat-induction-ext,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
top: Top,
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
DCC-order-type-less,
lifting-strict-spread,
has-value_wf_base,
base_wf,
is-exception_wf,
top_wf,
equal_wf,
lifting-strict-less,
strict4-decide,
strict4-spread,
bool_cases_sqequal,
complete-nat-induction-ext
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueApply,
baseApply,
closedConclusion,
hypothesisEquality,
applyExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
inlFormation,
because_Cache,
sqequalSqle,
divergentSqle,
callbyvalueDecide,
unionEquality,
unionElimination,
sqleReflexivity,
dependent_functionElimination,
independent_functionElimination,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
callbyvalueSpread,
productEquality,
productElimination,
spreadExceptionCases
Latex:
DCC(WFO\{i:l\}();order-type-less())
Date html generated:
2018_05_21-PM-07_14_29
Last ObjectModification:
2018_05_19-PM-04_45_23
Theory : general
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