Nuprl Lemma : mtype-sqequal
∀[L:MutualRectypeSpec]. ∀[i:mKinds]. (mtype(L;i) ~ mrec(L;i))
Proof
Definitions occuring in Statement :
mtype: mtype(L;i),
mkinds: mKinds,
mrec: mrec(L;i),
mrec_spec: MutualRectypeSpec,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mtype: mtype(L;i),
mrec_spec: MutualRectypeSpec,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
mkinds: mKinds,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
or: P ∨ Q,
cons: [a / b],
decidable: Dec(P),
colength: colength(L),
nil: [],
it: ⋅,
guard: {T},
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
pi1: fst(t),
has-value: (a)↓
Lemmas referenced :
apply_alist-eager-map-atom,
list_wf,
pi1_wf,
istype-atom,
istype-void,
mkinds_wf,
mrec_spec_wf,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
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,
istype-less_than,
list-cases,
eager_map_nil_lemma,
product_subtype_list,
colength-cons-not-zero,
colength_wf_list,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
istype-le,
subtract-1-ge-0,
subtype_base_sq,
intformeq_wf,
int_formula_prop_eq_lemma,
set_subtype_base,
int_subtype_base,
spread_cons_lemma,
decidable__equal_int,
subtract_wf,
itermSubtract_wf,
itermAdd_wf,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
le_wf,
eager_map_cons_lemma,
value-type-has-value,
top_wf,
list-value-type,
eager-map_wf,
product-value-type,
istype-nat,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
productEquality,
cumulativity,
atomEquality,
unionEquality,
universeEquality,
hypothesis,
hypothesisEquality,
Error :lambdaEquality_alt,
sqequalRule,
Error :productIsType,
Error :universeIsType,
Error :isect_memberEquality_alt,
voidElimination,
axiomSqEquality,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
dependent_functionElimination,
independent_pairFormation,
Error :functionIsTypeImplies,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
Error :equalityIstype,
because_Cache,
Error :dependent_set_memberEquality_alt,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
imageElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
intEquality,
sqequalBase,
callbyvalueReduce,
sqleReflexivity,
independent_pairEquality,
Error :functionIsType,
functionExtensionality
Latex:
\mforall{}[L:MutualRectypeSpec]. \mforall{}[i:mKinds]. (mtype(L;i) \msim{} mrec(L;i))
Date html generated:
2019_06_20-PM-02_14_53
Last ObjectModification:
2019_02_28-PM-02_06_33
Theory : tuples
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