Nuprl Lemma : callbyvalueall_seq-shift-init0
∀[L,F,K:Top]. ∀[m,n,p:ℕ].
(callbyvalueall_seq(L;λf.mk_applies(f;K;p);F;n;m)
~ callbyvalueall_seq(λi.mk_applies(L i;K;p);λx.x;λg.(F (λf.(g mk_applies(f;K;p))));n;m))
Proof
Definitions occuring in Statement :
mk_applies: mk_applies(F;G;m),
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
mk_applies: mk_applies(F;G;m),
primrec: primrec(n;b;c),
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
callbyvalueall_seq-shift-init,
false_wf,
le_wf,
add-zero,
subtype_base_sq,
subtype_rel_self,
nat_wf,
top_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
setElimination,
rename,
instantiate,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[L,F,K:Top]. \mforall{}[m,n,p:\mBbbN{}].
(callbyvalueall\_seq(L;\mlambda{}f.mk\_applies(f;K;p);F;n;m)
\msim{} callbyvalueall\_seq(\mlambda{}i.mk\_applies(L i;K;p);\mlambda{}x.x;\mlambda{}g.(F (\mlambda{}f.(g mk\_applies(f;K;p))));n;m))
Date html generated:
2016_05_15-PM-02_13_29
Last ObjectModification:
2015_12_27-AM-00_33_13
Theory : untyped!computation
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