Nuprl Lemma : callbyvalueall-single
∀[F,a:Top]. (let x ⟵ [a] in F[x] ~ let x ⟵ a in F[[a]])
Proof
Definitions occuring in Statement :
cons: [a / b],
nil: [],
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
cons: [a / b],
nil: [],
it: ⋅,
all: ∀x:A. B[x],
implies: P ⇒ Q,
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,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
sq_type: SQType(T)
Lemmas referenced :
evalall_nil_lemma,
base_wf,
lifting-strict-callbyvalue,
has-value_wf_base,
is-exception_wf,
evalall-sqequal,
subtype_base_sq,
subtype_rel_self,
equal_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
sqleReflexivity,
extract_by_obid,
hypothesis,
thin,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
lambdaFormation,
sqequalHypSubstitution,
isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
callbyvalueCallbyvalue,
callbyvalueExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalSqle,
divergentSqle,
instantiate,
cumulativity,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
sqleRule,
axiomSqleEquality,
equalityTransitivity,
equalitySymmetry,
sqequalAxiom
Latex:
\mforall{}[F,a:Top]. (let x \mleftarrow{}{} [a] in F[x] \msim{} let x \mleftarrow{}{} a in F[[a]])
Date html generated:
2017_10_01-AM-08_39_37
Last ObjectModification:
2017_07_26-PM-04_27_37
Theory : untyped!computation
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