Nuprl Lemma : spread-sq-pi12
∀[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,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
prop: ℙ,
strict4: strict4(F),
and: P ∧ Q
Lemmas referenced :
top_wf,
base_wf,
strict4_wf,
spread-sqle-pi12,
pi12-sqle-spread
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
hypothesis,
because_Cache,
lambdaFormation,
sqequalAxiom,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_functionElimination
Latex:
\mforall{}[t:Top]. \mforall{}[P:Base]. P[fst(t);snd(t)] \msim{} 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_32
Last ObjectModification:
2016_01_14-PM-07_11_03
Theory : call!by!value_2
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