Nuprl Lemma : mon_htfor_cons_lemma
∀f,as,a,g,T:Top. (HTFor{g} h::t ∈ [a / as]. f[h;t] ~ f[a;as] * (HTFor{g} h::t ∈ as. f[h;t]))
Proof
Definitions occuring in Statement :
mon_htfor: HTFor{g} h::t ∈ as. f[h; t],
cons: [a / b],
top: Top,
infix_ap: x f y,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
sqequal: s ~ t,
grp_op: *
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
mon_htfor: HTFor{g} h::t ∈ as. f[h; t],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
infix_ap: x f y
Lemmas referenced :
top_wf,
for_hdtl_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{}f,as,a,g,T:Top. (HTFor\{g\} h::t \mmember{} [a / as]. f[h;t] \msim{} f[a;as] * (HTFor\{g\} h::t \mmember{} as. f[h;t]))
Date html generated:
2016_05_16-AM-07_36_38
Last ObjectModification:
2015_12_28-PM-05_45_31
Theory : list_2
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