Nuprl Lemma : callbyvalueall-single-sqle2
∀[F,G:Base]. ∀[a:Top]. let x ⟵ [a] in G[x] ≤ let x ⟵ a in F[x] supposing ∀b:Base. (G[[b]] ≤ F[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 :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
prop: ℙ,
top: Top,
callbyvalueall: callbyvalueall,
has-valueall: has-valueall(a),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
has-valueall_wf_base,
evalall-sqequal,
cbv_sqle,
callbyvalueall-single,
top_wf,
sqle_wf_base,
base_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
because_Cache,
isect_memberFormation,
introduction,
axiomSqleEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
voidEquality,
sqleRule,
independent_isectElimination,
lambdaFormation,
dependent_functionElimination,
sqleReflexivity
Latex:
\mforall{}[F,G:Base]. \mforall{}[a:Top]. let x \mleftarrow{}{} [a] in G[x] \mleq{} let x \mleftarrow{}{} a in F[x] supposing \mforall{}b:Base. (G[[b]] \mleq{} F[b])
Date html generated:
2016_05_15-PM-02_08_56
Last ObjectModification:
2016_01_15-PM-10_21_34
Theory : untyped!computation
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