Nuprl Lemma : lifting-isaxiom-concat
∀[a,b,c:Top]. (concat(if a = Ax then b otherwise c) ~ if a = Ax then concat(b) otherwise concat(c))
Proof
Definitions occuring in Statement :
concat: concat(ll),
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,
top: Top,
guard: {T},
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
uimplies: b supposing a
Lemmas referenced :
lifting-strict-isaxiom,
strict4-concat,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
baseClosed,
voidElimination,
voidEquality,
independent_isectElimination
Latex:
\mforall{}[a,b,c:Top]. (concat(if a = Ax then b otherwise c) \msim{} if a = Ax then concat(b) otherwise concat(c))
Date html generated:
2016_05_15-PM-02_07_23
Last ObjectModification:
2016_01_15-PM-10_24_02
Theory : untyped!computation
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