Nuprl Lemma : cbv_sqle
∀[a,X,Y:Base]. eval x = a in X[x] ≤ eval x = a in Y[x] supposing (a)↓ ⇒ (X[a] ≤ Y[a])
Proof
Definitions occuring in Statement :
has-value: (a)↓,
callbyvalue: callbyvalue,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
base_wf,
sqle_wf_base,
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,
independent_functionElimination,
thin,
callbyvalueExceptionCases,
axiomSqleEquality,
exceptionSqequal,
sqleReflexivity,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
lemma_by_obid,
isectElimination,
functionEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,X,Y:Base]. eval x = a in X[x] \mleq{} eval x = a in Y[x] supposing (a)\mdownarrow{} {}\mRightarrow{} (X[a] \mleq{} Y[a])
Date html generated:
2016_05_13-PM-03_45_45
Last ObjectModification:
2016_01_14-PM-07_06_40
Theory : computation
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