Nuprl Lemma : length_of_cons_lemma
∀as,a:Top. (||[a / as]|| ~ ||as|| + 1)
Proof
Definitions occuring in Statement :
length: ||as||,
cons: [a / b],
top: Top,
all: ∀x:A. B[x],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
length: ||as||,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
top_wf,
list_ind_cons_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{}as,a:Top. (||[a / as]|| \msim{} ||as|| + 1)
Date html generated:
2016_05_14-AM-06_32_58
Last ObjectModification:
2015_12_26-PM-00_37_34
Theory : list_0
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