Nuprl Lemma : fix-not-exception
∀[G,g:Base]. ¬is-exception(G fix(g)) supposing ∀j:ℕ. (¬is-exception(G (g^j ⊥)))
Proof
Definitions occuring in Statement :
fun_exp: f^n,
nat: ℕ,
bottom: ⊥,
is-exception: is-exception(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
apply: f a,
fix: fix(F),
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
is-exception: is-exception(t),
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
base_wf,
int_subtype_base,
le_wf,
set_subtype_base,
not_wf,
nat_wf,
all_wf,
is-exception_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
exceptionCompactness,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
voidElimination,
because_Cache,
lemma_by_obid,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
lambdaEquality,
applyEquality,
intEquality,
natural_numberEquality,
independent_isectElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[G,g:Base]. \mneg{}is-exception(G fix(g)) supposing \mforall{}j:\mBbbN{}. (\mneg{}is-exception(G (g\^{}j \mbot{})))
Date html generated:
2016_05_14-AM-06_09_55
Last ObjectModification:
2016_01_14-PM-07_50_08
Theory : partial_1
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