Nuprl Lemma : lifting-isaxiom-isaxiom
∀[a,b,c,d,e:Top].
(if if a = Ax then b otherwise c = Ax then d otherwise e
~ if a = Ax then if b = Ax then d otherwise e otherwise if c = Ax then d otherwise e)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x]
,
top: Top
,
isaxiom: if z = Ax then a otherwise b
,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w])
,
so_apply: x[s1;s2;s3;s4]
,
top: Top
,
uimplies: b supposing a
,
strict4: strict4(F)
,
and: P ∧ Q
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
has-value: (a)↓
,
prop: ℙ
,
guard: {T}
,
or: P ∨ Q
,
squash: ↓T
Lemmas referenced :
top_wf,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-isaxiom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueIsaxiom,
hypothesis,
baseApply,
closedConclusion,
hypothesisEquality,
isaxiomExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[a,b,c,d,e:Top].
(if if a = Ax then b otherwise c = Ax then d otherwise e
\msim{} if a = Ax then if b = Ax then d otherwise e otherwise if c = Ax then d otherwise e)
Date html generated:
2016_05_13-PM-03_42_13
Last ObjectModification:
2016_01_14-PM-07_08_48
Theory : computation
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