Nuprl Lemma : fpf-union-join-ap
∀[f,g,eq,x,R:Top]. (fpf-union-join(eq;R;f;g)(x) ~ fpf-union(f;g;eq;R;x))
Proof
Definitions occuring in Statement :
fpf-union-join: fpf-union-join(eq;R;f;g),
fpf-union: fpf-union(f;g;eq;R;x),
fpf-ap: f(x),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
fpf-union-join: fpf-union-join(eq;R;f;g),
fpf-ap: f(x),
pi2: snd(t),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
lemma_by_obid,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality
Latex:
\mforall{}[f,g,eq,x,R:Top]. (fpf-union-join(eq;R;f;g)(x) \msim{} fpf-union(f;g;eq;R;x))
Date html generated:
2018_05_21-PM-09_23_28
Last ObjectModification:
2018_02_09-AM-10_19_20
Theory : finite!partial!functions
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