Nuprl Lemma : trivial-subterm
∀[opr:Type]. ∀f:opr. ∀bts:bound-term(opr) List. ∀i:ℕ||bts||.  snd(bts[i]) << mkterm(f;bts)
Proof
Definitions occuring in Statement : 
subterm: s << t
, 
bound-term: bound-term(opr)
, 
mkterm: mkterm(opr;bts)
, 
select: L[n]
, 
length: ||as||
, 
list: T List
, 
int_seg: {i..j-}
, 
uall: ∀[x:A]. B[x]
, 
pi2: snd(t)
, 
all: ∀x:A. B[x]
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
int_seg: {i..j-}
, 
uimplies: b supposing a
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
le: A ≤ B
, 
less_than: a < b
, 
squash: ↓T
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
prop: ℙ
, 
bound-term: bound-term(opr)
, 
pi2: snd(t)
, 
immediate-subterm: s < t
, 
cand: A c∧ B
Lemmas referenced : 
immediate-is-subterm, 
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, 
mkterm_wf, 
term_wf, 
int_seg_wf, 
list_wf, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
lambdaFormation_alt, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
dependent_functionElimination, 
hypothesis, 
setElimination, 
rename, 
because_Cache, 
independent_isectElimination, 
productElimination, 
imageElimination, 
natural_numberEquality, 
unionElimination, 
approximateComputation, 
independent_functionElimination, 
dependent_pairFormation_alt, 
lambdaEquality_alt, 
int_eqEquality, 
Error :memTop, 
sqequalRule, 
independent_pairFormation, 
universeIsType, 
voidElimination, 
inhabitedIsType, 
equalityIstype, 
equalityTransitivity, 
equalitySymmetry, 
productIsType, 
instantiate, 
universeEquality
Latex:
\mforall{}[opr:Type].  \mforall{}f:opr.  \mforall{}bts:bound-term(opr)  List.  \mforall{}i:\mBbbN{}||bts||.    snd(bts[i])  <<  mkterm(f;bts)
Date html generated:
2020_05_19-PM-09_54_17
Last ObjectModification:
2020_03_10-PM-01_46_13
Theory : terms
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