Nuprl Lemma : is-list-map
∀[t,f:Top]. (is-list(map(f;t)) ~ is-list(t))
Proof
Definitions occuring in Statement :
is-list: is-list(t),
map: map(f;as),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
map: map(f;as),
list_ind: list_ind,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
is-list: is-list(t),
pi2: snd(t),
btrue: tt,
it: ⋅,
fun_exp: f^n,
primrec: primrec(n;b;c),
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
strict4: strict4(F),
has-value: (a)↓,
guard: {T},
squash: ↓T,
subtype_rel: A ⊆r B,
cons: [a / b],
nil: []
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_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,
ge_wf,
less_than_wf,
base_wf,
strictness-apply,
strictness-callbyvalue,
bottom-sqle,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
fun_exp_unroll_1,
top_wf,
lifting-strict-callbyvalue,
has-value_wf_base,
is-exception_wf,
cbv_sqle,
int_subtype_base,
has-value-implies-dec-ispair-2,
has-value-implies-dec-isaxiom-2,
cbv_bottom_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
sqequalSqle,
lambdaFormation,
fixpointLeast,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomSqleEquality,
unionElimination,
dependent_set_memberEquality,
because_Cache,
sqequalAxiom,
baseClosed,
callbyvalueCallbyvalue,
callbyvalueReduce,
baseApply,
closedConclusion,
callbyvalueExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
instantiate,
applyEquality,
sqleReflexivity,
divergentSqle
Latex:
\mforall{}[t,f:Top]. (is-list(map(f;t)) \msim{} is-list(t))
Date html generated:
2018_05_21-PM-10_18_53
Last ObjectModification:
2017_02_27-PM-02_08_08
Theory : eval!all
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