Nuprl Lemma : callbyvalueall-single-sqle
∀[F,G:Base]. ∀[a:Top]. let x ⟵ a in F[x] ≤ let x ⟵ [a] in G[x] supposing ∀b:Base. (F[b] ≤ G[[b]])
Proof
Definitions occuring in Statement :
cons: [a / b],
nil: [],
callbyvalueall: callbyvalueall,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
top: Top,
so_apply: x[s],
callbyvalueall: callbyvalueall,
uimplies: b supposing a,
has-valueall: has-valueall(a),
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
top_wf,
sqle_wf_base,
base_wf,
all_wf,
has-valueall_wf_base,
evalall-sqequal,
cbv_sqle,
callbyvalueall-single
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
sqleRule,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
lambdaFormation,
dependent_functionElimination,
because_Cache,
sqleReflexivity,
lambdaEquality,
isect_memberFormation,
introduction,
axiomSqleEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[F,G:Base]. \mforall{}[a:Top]. let x \mleftarrow{}{} a in F[x] \mleq{} let x \mleftarrow{}{} [a] in G[x] supposing \mforall{}b:Base. (F[b] \mleq{} G[[b]])
Date html generated:
2016_05_15-PM-02_08_54
Last ObjectModification:
2016_01_15-PM-10_21_40
Theory : untyped!computation
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