Nuprl Lemma : cbv_sqle_2
∀[a,b,X,Y:Base].
eval x = a in
X[x] ≤ eval x = b in
Y[x]
supposing ((a)↓ ⇒ (X[a] ≤ eval x = b in Y[x]))
∧ (∀u,v:Base. ((a ~ exception(u; v)) ⇒ (eval x = b in Y[x] ~ 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],
implies: P ⇒ Q,
and: P ∧ Q,
base: Base,
sqle: s ≤ t,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
all: ∀x:A. B[x]
Lemmas referenced :
base_wf,
all_wf,
sqle_wf_base,
and_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
divergentSqle,
callbyvalueCallbyvalue,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
callbyvalueReduce,
productElimination,
thin,
independent_functionElimination,
callbyvalueExceptionCases,
axiomSqleEquality,
exceptionSqequal,
sqleReflexivity,
lemma_by_obid,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
functionEquality,
lambdaEquality,
sqequalIntensionalEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination
Latex:
\mforall{}[a,b,X,Y:Base].
eval x = a in
X[x] \mleq{} eval x = b in
Y[x]
supposing ((a)\mdownarrow{} {}\mRightarrow{} (X[a] \mleq{} eval x = b in Y[x]))
\mwedge{} (\mforall{}u,v:Base. ((a \msim{} exception(u; v)) {}\mRightarrow{} (eval x = b in Y[x] \msim{} exception(u; v))))
Date html generated:
2016_05_13-PM-03_45_48
Last ObjectModification:
2016_01_14-PM-07_06_50
Theory : computation
Home
Index