Nuprl Lemma : simple-cbva-seq-spread0
∀[F,G,H,L:Top]. (let x,y = simple-cbva-seq(L;<F, G>;0) in H[x;y] ~ simple-cbva-seq(L;H[F;G];0))
Proof
Definitions occuring in Statement :
simple-cbva-seq: simple-cbva-seq(L;F;m),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
spread: spread def,
pair: <a, b>,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
simple-cbva-seq: simple-cbva-seq(L;F;m),
cbva-seq: cbva-seq(L;F;m),
callbyvalueall-seq: callbyvalueall-seq(L;G;F;n;m),
ifthenelse: if b then t else f fi ,
le_int: i ≤z j,
bnot: ¬bb,
lt_int: i <z j,
bfalse: ff,
btrue: tt,
eq_int: (i =z j),
subtract: n - m,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
false: False,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
btrue_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
top_wf,
eqff_to_assert,
le_int_wf,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
hypothesis,
thin,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
natural_numberEquality,
because_Cache,
isect_memberFormation,
sqequalAxiom,
isect_memberEquality,
hypothesisEquality,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
lambdaEquality,
intEquality,
voidEquality,
computeAll
Latex:
\mforall{}[F,G,H,L:Top]. (let x,y = simple-cbva-seq(L;<F, G>0) in H[x;y] \msim{} simple-cbva-seq(L;H[F;G];0))
Date html generated:
2017_10_01-AM-08_41_25
Last ObjectModification:
2017_07_26-PM-04_28_38
Theory : untyped!computation
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