Nuprl Lemma : subterm-size
∀[opr:Type]. ∀[s,t:term(opr)]. (s << t ⇒ term-size(s) < term-size(t))
Proof
Definitions occuring in Statement :
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,
subterm: s << t,
subtype_rel: A ⊆r B,
rel_implies: R1 => R2,
all: ∀x:A. B[x],
infix_ap: x f y,
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
subterm-rel: subterm-rel(opr),
nat: ℕ
Lemmas referenced :
transitive-closure-minimal-ext,
immediate-subterm_wf,
less_than_wf,
term-size_wf,
immediate-subterm-size,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-less_than,
subterm_wf,
member-less_than,
term_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
because_Cache,
lambdaEquality_alt,
hypothesisEquality,
hypothesis,
inhabitedIsType,
applyEquality,
sqequalRule,
independent_functionElimination,
universeIsType,
dependent_functionElimination,
unionElimination,
imageElimination,
productElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
voidElimination,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
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_14
Last ObjectModification:
2020_03_09-PM-04_36_46
Theory : terms
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