Nuprl Lemma : l_ind_cons_lemma
∀A,x,b,a:Top. (l-ind([a / b];x;h,t,r.A[h;t;r]) ~ A[a;b;l-ind(b;x;h,t,r.A[h;t;r])])
Proof
Definitions occuring in Statement :
l-ind: l-ind(L;nilcase;h,t,r.F[h; t; r]),
cons: [a / b],
top: Top,
so_apply: x[s1;s2;s3],
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
l-ind: l-ind(L;nilcase;h,t,r.F[h; t; r]),
cons: [a / b]
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule
Latex:
\mforall{}A,x,b,a:Top. (l-ind([a / b];x;h,t,r.A[h;t;r]) \msim{} A[a;b;l-ind(b;x;h,t,r.A[h;t;r])])
Date html generated:
2016_05_14-AM-06_26_53
Last ObjectModification:
2015_12_26-PM-00_41_37
Theory : list_0
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