Nuprl Lemma : cbva_seq-sqequal-n
∀L:Top. ∀F1,F2:Base. ∀m,n:ℕ. ((F1 ~n + 1 F2) ⇒ (cbva_seq(L; F1; m) ~n cbva_seq(L; F2; m)))
Proof
Definitions occuring in Statement :
cbva_seq: cbva_seq(L; F; m),
nat: ℕ,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
add: n + m,
natural_number: $n,
base: Base,
sqequal_n: s ~n t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
cbva_seq: cbva_seq(L; F; m),
exists: ∃x:A. B[x],
true: True,
prop: ℙ,
mk_applies: mk_applies(F;G;m),
top: Top,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
uall: ∀[x:A]. B[x],
guard: {T},
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
sq_type: SQType(T),
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
callbyvalueall: callbyvalueall,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
decidable__lt,
true_wf,
primrec0_lemma,
false_wf,
le_wf,
nat_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
intformeq_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__equal_int,
itermAdd_wf,
int_term_value_add_lemma,
equal_wf,
subtype_base_sq,
int_subtype_base,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
add-subtract-cancel,
intformless_wf,
int_formula_prop_less_lemma,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
base_wf,
set_subtype_base,
all_wf,
sqequal_n_wf,
set_wf,
less_than_wf,
primrec-wf2,
top_wf,
mk_applies_roll
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequal_n rule,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
natural_numberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
unionElimination,
promote_hyp,
dependent_pairFormation,
baseClosed,
productElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
independent_pairFormation,
isectElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
because_Cache,
instantiate,
cumulativity,
independent_functionElimination,
equalityElimination,
sqequalnReflexivity,
baseApply,
closedConclusion,
applyEquality,
sqequalZero
Latex:
\mforall{}L:Top. \mforall{}F1,F2:Base. \mforall{}m,n:\mBbbN{}. ((F1 \msim{}n + 1 F2) {}\mRightarrow{} (cbva\_seq(L; F1; m) \msim{}n cbva\_seq(L; F2; m)))
Date html generated:
2017_10_01-AM-08_42_52
Last ObjectModification:
2017_07_26-PM-04_29_23
Theory : untyped!computation
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