Nuprl Lemma : p_first_nil_lemma
∀x:Top. (can-apply(p-first([]);x) ~ ff)
Proof
Definitions occuring in Statement :
p-first: p-first(L),
can-apply: can-apply(f;x),
nil: [],
bfalse: ff,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
p-first: p-first(L),
can-apply: can-apply(f;x),
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
isl: isl(x)
Lemmas referenced :
top_wf,
list_accum_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}x:Top. (can-apply(p-first([]);x) \msim{} ff)
Date html generated:
2016_05_15-PM-03_30_23
Last ObjectModification:
2015_12_27-PM-01_10_20
Theory : general
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