Nuprl Lemma : lifting-strict-spread
∀[F:Base]. ∀[p,q,r:Top].
∀[a,B:Top]. (F[let x,y = a in B[x;y];p;q;r] ~ let x,y = a in F[B[x;y];p;q;r]) supposing strict4(λx,y,z,w. F[x;y;z;w])
Proof
Definitions occuring in Statement :
strict4: strict4(F),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
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,
strict4: strict4(F),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
squash: ↓T,
or: P ∨ Q
Lemmas referenced :
top_wf,
equal_wf,
pair-eta,
has-value_wf_base,
is-exception_wf,
strict4_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
sqequalHypSubstitution,
sqequalRule,
productElimination,
hypothesis,
dependent_functionElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_functionElimination,
callbyvalueSpread,
equalityTransitivity,
equalitySymmetry,
productEquality,
extract_by_obid,
lambdaFormation,
sqleReflexivity,
isectElimination,
imageElimination,
unionElimination,
axiomSqleEquality,
spreadExceptionCases,
exceptionSqequal,
sqequalAxiom,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[F:Base]. \mforall{}[p,q,r:Top].
\mforall{}[a,B:Top]. (F[let x,y = a in B[x;y];p;q;r] \msim{} let x,y = a in F[B[x;y];p;q;r])
supposing strict4(\mlambda{}x,y,z,w. F[x;y;z;w])
Date html generated:
2017_04_14-AM-07_20_50
Last ObjectModification:
2017_02_27-PM-02_54_19
Theory : computation
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