Nuprl Lemma : concat-lifting-1-strict
∀[f:Top]. (f@ {} ~ {})
Proof
Definitions occuring in Statement :
concat-lifting-1: f@,
empty-bag: {},
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
concat-lifting-1: f@,
concat-lifting1: concat-lifting1(f;bag),
concat-lifting: concat-lifting(n;f;bags),
concat-lifting-list: concat-lifting-list(n;bags),
bag-union: bag-union(bbs),
concat: concat(ll),
reduce: reduce(f;k;as),
list_ind: list_ind,
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
ifthenelse: if b then t else f fi ,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
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,
eq_int: (i =z j),
bfalse: ff,
bag-combine: ⋃x∈bs.f[x],
bag-map: bag-map(f;bs),
map: map(f;as),
empty-bag: {},
nil: [],
it: ⋅
Lemmas referenced :
top_wf,
lifting-strict-ispair,
lifting-strict-callbyvalue,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-decide
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
baseApply,
closedConclusion,
hypothesisEquality,
callbyvalueExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
because_Cache,
sqequalAxiom
Latex:
\mforall{}[f:Top]. (f@ \{\} \msim{} \{\})
Date html generated:
2016_05_15-PM-03_07_58
Last ObjectModification:
2016_01_16-AM-08_34_05
Theory : bags
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