Nuprl Lemma : pi12-sqle-spread
∀[t:Top]. ∀[P:Base]. P[fst(t);snd(t)] ≤ let x,y = t in P[x;y] supposing strict4(λx,y,z,w. P[x;y])
Proof
Definitions occuring in Statement :
strict4: strict4(F),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
pi1: fst(t),
pi2: snd(t),
lambda: λx.A[x],
spread: spread def,
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
pi1: fst(t),
prop: ℙ,
top: Top,
has-value: (a)↓,
pi2: snd(t),
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
lifting-strict-spread,
is-exception_wf,
has-value_wf_base,
pair-eta,
top_wf,
base_wf,
strict4_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
axiomSqleEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
voidElimination,
voidEquality,
sqleRule,
divergentSqle,
callbyvalueSpread,
sqleReflexivity,
spreadExceptionCases,
exceptionSqequal,
independent_isectElimination
Latex:
\mforall{}[t:Top]. \mforall{}[P:Base]. P[fst(t);snd(t)] \mleq{} let x,y = t in P[x;y] supposing strict4(\mlambda{}x,y,z,w. P[x;y])
Date html generated:
2016_05_13-PM-03_46_28
Last ObjectModification:
2016_01_14-PM-07_11_05
Theory : call!by!value_2
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