Nuprl Lemma : mon_for_cons_lemma
∀f,as,a,g,T:Top. (For{g} x ∈ [a / as]. f[x] ~ f[a] * (For{g} x ∈ as. f[x]))
Proof
Definitions occuring in Statement :
mon_for: For{g} x ∈ as. f[x],
cons: [a / b],
top: Top,
infix_ap: x f y,
so_apply: x[s],
all: ∀x:A. B[x],
sqequal: s ~ t,
grp_op: *
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
mon_for: For{g} x ∈ as. f[x],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
infix_ap: x f y
Lemmas referenced :
top_wf,
for_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. (For\{g\} x \mmember{} [a / as]. f[x] \msim{} f[a] * (For\{g\} x \mmember{} as. f[x]))
Date html generated:
2016_05_16-AM-07_35_59
Last ObjectModification:
2015_12_28-PM-05_45_39
Theory : list_2
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