Nuprl Lemma : dl-diamond-unwind-1
∀a:Prog. ∀phi:Prop. |= <(a)*> phi ⇒ (phi ∨ <a> (phi ⇒ 0) ∨ <(a)*> phi)
Proof
Definitions occuring in Statement :
dl-valid: |= phi,
dl-diamond: <x1> x,
dl-or: x1 ∨ x,
dl-implies: x1 ⇒ x,
dl-false: 0,
dl-iterate: (x)*,
dl-prop: Prop,
dl-prog: Prog,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
dl-valid: |= phi,
dl-prop-sem: [|phi|],
dl-sem: dl-sem(K;n.R[n];m.P[m]),
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
top: Top,
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
dl-prog-sem: [|alpha|],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
rel_star: R^*,
infix_ap: x f y,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
false: False,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
rel_exp: R^n,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T},
cand: A c∧ B
Lemmas referenced :
dl-ind-dl-implies,
istype-void,
dl-ind-dl-diamond,
dl-ind-dl-iterate,
dl-ind-dl-or,
dl-ind-dl-false,
rel_star_wf,
dl-prog-sem_wf,
istype-nat,
subtype_rel_self,
dl-prop-sem_wf,
istype-universe,
dl-prop_wf,
dl-prog_wf,
rel_exp_wf,
istype-le,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
istype-less_than,
primrec-wf2,
false_wf,
rel_exp_add_iff,
decidable__equal_int,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
subtype_base_sq,
int_subtype_base,
rel_exp1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
productElimination,
productIsType,
because_Cache,
universeIsType,
applyEquality,
hypothesisEquality,
lambdaEquality_alt,
instantiate,
universeEquality,
functionIsType,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
rename,
setElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
unionIsType,
inhabitedIsType,
setIsType,
functionEquality,
unionEquality,
productEquality,
inlFormation_alt,
hyp_replacement,
equalitySymmetry,
cumulativity,
intEquality,
equalityTransitivity,
inrFormation_alt
Latex:
\mforall{}a:Prog. \mforall{}phi:Prop. |= <(a)*> phi {}\mRightarrow{} (phi \mvee{} <a> (phi {}\mRightarrow{} 0) \mvee{} <(a)*> phi)
Date html generated:
2019_10_15-AM-11_46_36
Last ObjectModification:
2019_04_25-PM-01_18_50
Theory : dynamic!logic
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