Nuprl Lemma : cbv-reduce-strict
∀[F,a,B:Base].
F[eval x = a in
B[x]] ≤ F[B[a]]
supposing (∀x:Base. ((F[x])↓ ⇒ (x)↓))
∧ (∀u,v,x:Base. ((F[x] ~ exception(u; v)) ⇒ (↓(x ~ exception(u; v)) ∨ (x)↓)))
∧ (∀u,v:Base. (B[exception(u; v)] ~ exception(u; v)))
Proof
Definitions occuring in Statement :
has-value: (a)↓,
callbyvalue: callbyvalue,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
base: Base,
sqle: s ≤ t,
sqequal: s ~ t
Definitions unfolded in proof :
uimplies: b supposing a,
or: P ∨ Q,
all: ∀x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
has-value: (a)↓,
squash: ↓T,
top: Top,
is-exception: is-exception(t)
Lemmas referenced :
bottom-sqle,
has-value_wf_base,
is-exception_wf,
all_wf,
base_wf,
squash_wf,
or_wf,
sqequal-wf-base
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
axiomSqleEquality,
introduction,
isect_memberFormation,
sqequalIntensionalEquality,
because_Cache,
functionEquality,
lambdaEquality,
productEquality,
hypothesis,
hypothesisEquality,
baseClosed,
closedConclusion,
baseApply,
sqequalRule,
isectElimination,
lemma_by_obid,
cut,
divergentSqle,
thin,
productElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
sqleReflexivity,
callbyvalueReduce,
callbyvalueCallbyvalue,
independent_functionElimination,
dependent_functionElimination,
exceptionSqequal,
imageElimination,
unionElimination,
callbyvalueExceptionCases,
voidEquality,
voidElimination,
sqleRule
Latex:
\mforall{}[F,a,B:Base].
F[eval x = a in
B[x]] \mleq{} F[B[a]]
supposing (\mforall{}x:Base. ((F[x])\mdownarrow{} {}\mRightarrow{} (x)\mdownarrow{}))
\mwedge{} (\mforall{}u,v,x:Base. ((F[x] \msim{} exception(u; v)) {}\mRightarrow{} (\mdownarrow{}(x \msim{} exception(u; v)) \mvee{} (x)\mdownarrow{})))
\mwedge{} (\mforall{}u,v:Base. (B[exception(u; v)] \msim{} exception(u; v)))
Date html generated:
2019_06_20-AM-11_20_42
Last ObjectModification:
2018_10_15-PM-03_28_17
Theory : call!by!value_1
Home
Index