Nuprl Lemma : lifting-strict-callbyvalue
∀[F:Base]. ∀[p,q,r:Top]. ∀[a,B:Top]. (F[eval x = a in B[x];p;q;r] ~ eval x = a in F[B[x];p;q;r]) supposing strict4(λx,\000Cy,z,w. F[x;y;z;w])
Proof
Definitions occuring in Statement :
strict4: strict4(F),
callbyvalue: callbyvalue,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3;s4],
so_apply: x[s],
lambda: λx.A[x],
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
squash: ↓T,
or: P ∨ Q,
prop: ℙ
Lemmas referenced :
base_wf,
strict4_wf,
top_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
sqequalHypSubstitution,
sqequalRule,
productElimination,
hypothesis,
dependent_functionElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_functionElimination,
callbyvalueCallbyvalue,
callbyvalueReduce,
sqleReflexivity,
lemma_by_obid,
isectElimination,
imageElimination,
unionElimination,
axiomSqleEquality,
callbyvalueExceptionCases,
exceptionSqequal,
sqequalAxiom,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[F:Base]. \mforall{}[p,q,r:Top].
\mforall{}[a,B:Top]. (F[eval x = a in B[x];p;q;r] \msim{} eval x = a in F[B[x];p;q;r]) supposing strict4(\mlambda{}x,y,z,\000Cw. F[x;y;z;w])
Date html generated:
2016_05_13-PM-03_41_52
Last ObjectModification:
2016_01_14-PM-07_08_58
Theory : computation
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