Nuprl Lemma : term-cases
∀[opr:Type]
∀t:term(opr)
((∃v:varname(). ((¬(v = nullvar() ∈ varname())) ∧ (t = varterm(v) ∈ term(opr))))
∨ (∃f:opr. ∃bts:{bt:bound-term(opr)| bound-term-size(bt) < term-size(t)} List. (t = mkterm(f;bts) ∈ term(opr))))
Proof
Definitions occuring in Statement :
bound-term-size: bound-term-size(bt),
bound-term: bound-term(opr),
term-size: term-size(t),
mkterm: mkterm(opr;bts),
varterm: varterm(v),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
implies: P ⇒ Q,
coterm-fun: coterm-fun(opr;T),
or: P ∨ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
false: False,
varterm: varterm(v),
nat: ℕ,
prop: ℙ,
bound-term: bound-term(opr),
mkterm: mkterm(opr;bts),
so_lambda: λ2x.t[x],
so_apply: x[s],
bound-term-size: bound-term-size(bt),
sq_stable: SqStable(P),
decidable: Dec(P),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
squash: ↓T,
le: A ≤ B
Lemmas referenced :
term-ext,
subtype_rel_weakening,
term_wf,
coterm-fun_wf,
ext-eq_inversion,
nullvar_wf,
varterm_wf,
istype-void,
list_wf,
bound-term_wf,
less_than_wf,
bound-term-size_wf,
term-size_wf,
mkterm_wf,
subtype_rel_list,
varname_wf,
istype-less_than,
list-subtype,
l_member_wf,
subtype_rel_sets,
term_size_mkterm_lemma,
istype-universe,
summand-le-lsum,
sq_stable__le,
decidable__le,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_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_not_lemma,
int_formula_prop_wf,
decidable__lt,
lsum_wf,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
inhabitedIsType,
unionElimination,
inlFormation_alt,
dependent_pairFormation_alt,
setElimination,
rename,
independent_functionElimination,
voidElimination,
equalityIstype,
because_Cache,
independent_pairFormation,
productIsType,
functionIsType,
equalityTransitivity,
equalitySymmetry,
universeIsType,
setEquality,
lambdaEquality_alt,
productEquality,
setIsType,
productElimination,
inrFormation_alt,
dependent_functionElimination,
Error :memTop,
instantiate,
universeEquality,
natural_numberEquality,
applyLambdaEquality,
approximateComputation,
int_eqEquality,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_set_memberEquality_alt,
addEquality
Latex:
\mforall{}[opr:Type]
\mforall{}t:term(opr)
((\mexists{}v:varname(). ((\mneg{}(v = nullvar())) \mwedge{} (t = varterm(v))))
\mvee{} (\mexists{}f:opr
\mexists{}bts:\{bt:bound-term(opr)| bound-term-size(bt) < term-size(t)\} List. (t = mkterm(f;bts))))
Date html generated:
2020_05_19-PM-09_54_00
Last ObjectModification:
2020_03_09-PM-04_08_27
Theory : terms
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