Nuprl Lemma : term-ext
∀[opr:Type]. term(opr) ≡ coterm-fun(opr;term(opr))
Proof
Definitions occuring in Statement :
term: term(opr),
coterm-fun: coterm-fun(opr;T),
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
term: term(opr),
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
coterm-fun: coterm-fun(opr;T),
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
not: ¬A,
false: False,
coterm-size: coterm-size(t),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
or: P ∨ Q,
has-value: (a)↓,
lsum: Σ(f[x] | x ∈ L),
l_sum: l_sum(L),
reduce: reduce(f;k;as),
list_ind: list_ind,
map: map(f;as),
nil: [],
it: ⋅,
cons: [a / b],
le: A ≤ B,
less_than': less_than'(a;b),
colength: colength(L),
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
pi2: snd(t)
Lemmas referenced :
coterm-ext,
term_wf,
coterm-fun_wf,
istype-universe,
subtype_rel_weakening,
coterm_wf,
ext-eq_inversion,
list_wf,
varname_wf,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
istype-int,
int-value-type,
coterm-size_wf,
nullvar_wf,
istype-void,
nat_properties,
full-omega-unsat,
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,
istype-less_than,
list-cases,
product_subtype_list,
colength-cons-not-zero,
colength_wf_list,
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,
intformnot_wf,
itermSubtract_wf,
itermAdd_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
decidable__le,
lsum_cons_lemma,
istype-nat,
nil_wf,
istype-sqle,
l_sum-wf-partial-nat,
map_wf,
partial_wf,
pi2_wf,
add-wf-partial-nat,
nat-partial-nat,
istype-false,
add-has-value-iff,
cons_wf,
subtype_rel_list,
subtype_rel_product,
has-value_wf_base,
is-exception_wf,
map_cons_lemma,
reduce_cons_lemma,
add-swap,
reduce_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_pairFormation,
lambdaEquality_alt,
universeIsType,
hypothesis,
sqequalRule,
productElimination,
independent_pairEquality,
axiomEquality,
instantiate,
universeEquality,
setElimination,
rename,
applyEquality,
independent_isectElimination,
inhabitedIsType,
lambdaFormation_alt,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
inlEquality_alt,
productIsType,
productEquality,
intEquality,
natural_numberEquality,
inrEquality_alt,
setIsType,
functionIsType,
because_Cache,
intWeakElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
voidElimination,
functionIsTypeImplies,
promote_hyp,
hypothesis_subsumption,
dependent_set_memberEquality_alt,
applyLambdaEquality,
imageElimination,
baseApply,
closedConclusion,
baseClosed,
sqequalBase,
divergentSqle,
sqleReflexivity,
axiomSqleEquality
Latex:
\mforall{}[opr:Type]. term(opr) \mequiv{} coterm-fun(opr;term(opr))
Date html generated:
2020_05_19-PM-09_53_35
Last ObjectModification:
2020_03_09-PM-04_08_11
Theory : terms
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