Nuprl Lemma : less-append
∀[a,b,c,d,L:Top]. (if (a) < (b) then c else d @ L ~ if (a) < (b) then c @ L else (d @ L))
Proof
Definitions occuring in Statement :
append: as @ bs,
uall: ∀[x:A]. B[x],
top: Top,
less: if (a) < (b) then c else d,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
member: t ∈ T,
so_apply: x[s1;s2;s3;s4],
top: Top,
uimplies: b supposing a
Lemmas referenced :
top_wf,
strict4-append,
lifting-strict-less
Rules used in proof :
sqequalSubstitution,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
hypothesisEquality
Latex:
\mforall{}[a,b,c,d,L:Top]. (if (a) < (b) then c else d @ L \msim{} if (a) < (b) then c @ L else (d @ L))
Date html generated:
2016_05_15-PM-02_07_51
Last ObjectModification:
2016_01_15-PM-10_22_03
Theory : untyped!computation
Home
Index