Nuprl Lemma : immediate-subterm-size
∀[opr:Type]. ∀[s,t:term(opr)]. (s < t ⇒ term-size(s) < term-size(t))
Proof
Definitions occuring in Statement :
immediate-subterm: s < t,
term-size: term-size(t),
term: term(opr),
less_than: a < b,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
immediate-subterm: s < t,
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
true: True,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
bound-term: bound-term(opr),
pi2: snd(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
ge: i ≥ j ,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
immediate-subterm_wf,
member-less_than,
term-size_wf,
term_wf,
istype-universe,
select_wf,
bound-term_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
length_wf,
intformless_wf,
int_formula_prop_less_lemma,
term_size_mkterm_lemma,
summand-le-lsum,
list_wf,
varname_wf,
pi2_wf,
l_member_wf,
sq_stable__le,
non_neg_length,
nat_properties,
istype-le,
list-subtype,
lsum_wf,
itermAdd_wf,
int_term_value_add_lemma,
less_than_wf,
squash_wf,
true_wf,
istype-nat,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
applyEquality,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_isectElimination,
functionIsTypeImplies,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality,
natural_numberEquality,
imageElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
voidElimination,
equalityIstype,
productEquality,
setIsType,
productIsType,
dependent_set_memberEquality_alt,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
setEquality,
addEquality,
closedConclusion
Latex:
\mforall{}[opr:Type]. \mforall{}[s,t:term(opr)]. (s < t {}\mRightarrow{} term-size(s) < term-size(t))
Date html generated:
2020_05_19-PM-09_54_05
Last ObjectModification:
2020_03_09-PM-04_08_30
Theory : terms
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