Nuprl Lemma : sqequal-fix-lemma1
∀[F,G,H:Base]. fix(F) fix(G) ~ fix((λx.(inl H[x]))) supposing ∀a,b:Base. (F a (G b) ~ inl H[a b])
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
inl: inl x,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
so_apply: x[s],
ge: i ≥ j ,
so_lambda: λ2x.t[x],
sq_type: SQType(T)
Latex:
\mforall{}[F,G,H:Base]. fix(F) fix(G) \msim{} fix((\mlambda{}x.(inl H[x]))) supposing \mforall{}a,b:Base. (F a (G b) \msim{} inl H[a b])
Date html generated:
2016_05_16-AM-10_50_40
Last ObjectModification:
2016_01_17-AM-11_07_55
Theory : halting!dataflow
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