Nuprl Lemma : spread-sqle-pi12
∀[P:Base]
∀[t:Top]. (let x,y = t in P[x;y] ≤ P[fst(t);snd(t)])
supposing ∀u,v:Base. (P[exception(u; v);exception(u; v)] ~ exception(u; v))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
spread: spread def,
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)↓,
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
base_wf,
all_wf,
top_wf,
is-exception_wf,
has-value_wf_base,
pair-eta
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqleRule,
thin,
divergentSqle,
callbyvalueSpread,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
sqleReflexivity,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
spreadExceptionCases,
axiomSqleEquality,
isect_memberEquality,
because_Cache,
lambdaEquality,
sqequalIntensionalEquality,
exceptionSqequal,
dependent_functionElimination
Latex:
\mforall{}[P:Base]
\mforall{}[t:Top]. (let x,y = t in P[x;y] \mleq{} P[fst(t);snd(t)])
supposing \mforall{}u,v:Base. (P[exception(u; v);exception(u; v)] \msim{} exception(u; v))
Date html generated:
2016_05_13-PM-03_46_30
Last ObjectModification:
2016_01_14-PM-07_11_04
Theory : call!by!value_2
Home
Index