Nuprl Lemma : decide-append
∀[d,F,G,L:Top]. (case d of inl(x) => F[x] | inr(y) => G[y] @ L ~ case d of inl(x) => F[x] @ L | inr(y) => G[y] @ L)
Proof
Definitions occuring in Statement :
append: as @ bs,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
append: as @ bs,
cons: [a / b],
list_ind: list_ind,
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,
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
Lemmas referenced :
top_wf,
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,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[d,F,G,L:Top].
(case d of inl(x) => F[x] | inr(y) => G[y] @ L \msim{} case d
of inl(x) =>
F[x] @ L
| inr(y) =>
G[y] @ L)
Date html generated:
2016_05_15-PM-02_07_49
Last ObjectModification:
2016_01_15-PM-10_22_06
Theory : untyped!computation
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