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
Lemmas :
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
decidable__lt,
add-associates,
add-swap,
add-commutes,
zero-add,
decidable__le,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
minus-add,
minus-minus,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
subtract-is-less,
lelt_wf,
subtype_base_sq,
nat_wf,
set_subtype_base,
int_subtype_base,
not-equal-2,
minus-zero,
all_wf,
base_wf,
sqequal-wf-base,
sqequal_n_wf,
int_seg_subtype-nat,
le-add-cancel-alt,
set_wf,
less_than_wf,
primrec-wf2,
sq_stable__le,
add-mul-special,
zero-mul
\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:
2015_07_17-AM-08_16_53
Last ObjectModification:
2015_01_27-AM-11_51_44
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