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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