Nuprl Lemma : lifting-strict-isaxiom
∀[F:Base]. ∀[p,q,r:Top].
∀[a,b,c:Top]. (F[if a = Ax then b otherwise c;p;q;r] ~ if a = Ax then F[b;p;q;r] otherwise F[c;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],
isaxiom: if z = Ax then a otherwise b,
lambda: λx.A[x],
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)↓,
or: P ∨ Q,
top: Top,
squash: ↓T,
prop: ℙ
Lemmas referenced :
base_wf,
strict4_wf,
top_wf,
is-exception_wf,
has-value_wf_base,
has-value-implies-dec-isaxiom-2
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,
callbyvalueIsaxiom,
lemma_by_obid,
unionElimination,
sqleReflexivity,
lambdaFormation,
because_Cache,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
axiomSqleEquality,
isaxiomExceptionCases,
exceptionSqequal,
isectElimination,
sqequalAxiom,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[F:Base]. \mforall{}[p,q,r:Top].
\mforall{}[a,b,c:Top].
(F[if a = Ax then b otherwise c;p;q;r] \msim{} if a = Ax then F[b;p;q;r] otherwise F[c;p;q;r])
supposing strict4(\mlambda{}x,y,z,w. F[x;y;z;w])
Date html generated:
2016_05_13-PM-03_41_35
Last ObjectModification:
2016_01_14-PM-07_08_59
Theory : computation
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